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You get up into high alpine forest at the top and the road parallels a high ridge/rim to the end where it turns to gravel. It is absolutely breath taking. You can see the desert floor in the distance and more of the mountain range as it falls off rapidly. If I posted the pix I have of this (I have posted 'em, before) they wouldn't do justice to the actual beauty of this place and the road is the best, curviest road I've ever ridden in Arizona. This is an awesome road! I wanna go back on the SV someday and take the gravel all the way to that lake, maybe tent camp there. It's just beautiful. If I lived around there, I'd spend all my free time in those mountains. 
Everyone does Clifton to Alpine. That's a pretty road, but it's not SQUAT to the road I just described, not even on the same plane with the road I just described. I mean, yeah, do the "Coronado trail" (what 191 Clifton to Alpine is called), too, but just don't miss 366, whatever you do. 
. I've ridden Utah once, can't help ya much with Utah. I just made the tourist destinations, Mt. Zion and Bryce Canyon parks. They were pretty and must sees, but that's the only area of the state I've been in. I need more seat time out there.
First, I HIGHLY recommend you get an annual National Park pass for each of you. I think they are $50. However, at $20 a pop per park, they pay for themselves real fast!! Also, when you reach the entrance, all you have to do is hand them the card and then you get in. You don't have to stop, get out your money, etc,... VERY convenient. The area where you will be riding is CRAMMED full of all kinds of National Parks!! Second, I would give serious consideration to trailering out to NM on I-40. Unload the bikes there, head into Southwestern NM and Southeastern Az, then start heading North into Utah. Run over into Colorado, then work your way back down to Albuquerque. There are several TWT people in that area (Jeffie Foo Foo, Cycle Cat) and they might be able to keep the truck and trailer while you are off riding. This will save your bodies and tires for the good stuff. And on that last day, you will be GLAD you are in the truck for the haul across West Texas instead of droning along on the bikes for mile after mile!! Been there done that... yay... 
Third, May is a good time to go in terms of low traffic and crowds, and also for low hotel rates because it is not the prime season yet. However, it can be very COLD in the mountains!! I would not be surprised if you get snowed on several times. You will definitely want good cold weather and rain gear! I have been snowed on in the middle of June 
I have been rained on pretty much every time I have been. Usually though the rain comes and goes pretty quick. It is not rain for days on end, all day long. I have spent a LOT of time staring at maps and potentially fun roads. 366 has been high on my list for some years. 191 is a fantastic ride. Part of what is great about it is the length of the ride. Deals Gap is what 11 miles or something? The stretch of 191 between Clifton and Alpine is 94 miles of bliss. We saw ONE other bike and ONE truck in the entire time. Also, the Morenci open pit copper mine is a sight to behold... We did the Petrified Forest and Painted Desert North of Alpine on our way North. Both very cool! Regarding the Grand Canyon, I would skip the South Rim in favor of the North Rim. MUCH less crowded and better views. Also, the run up US 89 Alt to Jacobs Lake rocks! There is nice camping there as well. The drop into Souther Utah is awesome with great views. Once in Utah, I would say that Zion National Park and Bryce Canyon National Park are both MUST sees. They are unlike anything you will see anywhere else on the planet!! Make sure you either have a LOT of film or a BIG memory card, whichever the case may be. You will need it! Here is some stuff from our trip out there back in 2001. Hwy 12 and 24 is easily one of the top rides in the country. Not only is the road incredible, the scenery is breathtaking and it changes constantly! It is one of those roads that needs to be done three times: once just to get over the amazement, once for the full on ride, and once to stop and take tons of pics! However, it is NOT a place where you want to risk leaving the pavement!!! Where 12 meets 24, there is the Capitol Reef National Park. Then if you run down Hwy 95 (yet another great ride) there is Natural Bridges National Monument. Hang a right on Hwy 261 and you'll reach the Mokee Dugway plateau drop. Go slow and the gravel is no big deal. The views are worth it! then if you head South on US 163 you will get to see Monument Valley. And if you want to see the Four Corners monument, just head back East on US 160. We turned North and went back up towards Moab. Tis a VERY cool place with lots to see and do. Got Deadhorse State Park, with a fantastic ride into the park and great views of the Colrado River from on high. There is Arches National Park, Canyon Land National Park, and more. If you go there, be sure to eat at Eddie McStiff's! Mmmm... 
They make good beer... We left and ran Northeast along the Colorado River on Hwy 128 up to I-70 and then scooted the short shot over to Fruita and the exit for the Colorado National Monument. This is another don't miss ride that has always been very popular with the groups I have led in the area. Okay, since you have 15 days... Wrap your head around the following! Just South of Grand Junction on US 50 you will see Hwy 141. Get gas before you head this way The run down through the canyons here is incredible. The cliffs are one single piece of rock! The road is twisting and great. Run it South all the way to Hwy 145 at Naturita (gas here). Run 145 South to Telluride, then on down to Cortez. Just East of Cortez on US 160 is the Mesa Verde National Park with the Cliff Dwellings. The road into the park is a blast and the cave dwellings are amazing. After this, keep East on US 160 to Durango. Run US 550 North all the way up through Silverton, Ouray, Ridgeway to Montrose. That right there would be a GOOD day ride. If you head East out of Montrose on US 50, there is the Black Canyon of the Gunnison National Park and it has some great camping right down on the river at the bottom of the gorge. The road down into the gorge is a 16% grade Lotta fun!! Next run US 50 East to Hwy 92 where you'll cross the Blue Mesa Reservoir Dam. Hwy 92 is another of those spectacular rides of which Colorado has so many! Run 92 all the way up to Hotchkiss and head West. Hit Hwy 65 and Head North over the Grand Mesa (get gas first). If you are wearing any mesh gear, you might want a liner or long sleeve shirt as it gets cool going over the Mesa. Run over the Mesa, through the canyon to I-70. Turn around and run it all the way back to Hwy 92. Yes... It is well worth the time!! Head East back to Hotchkiss and pick up Hwy 133. Get gas first because you DON'T want to buy any in Aspen! Run 133 up to 82, and head North to Glennwood Springs. I-70 East of Gleenwood Springs is actually a great ride. You just have to see it to understand. Even though it is freeway, the run through Glennwood Canyon is really awesome. A fun dip would be US 24 South then back up Hwy 91 to I-70 again. Keep heading East to Dillon on I-70 and pick up old US 6 East (on South side of I-70) and run this over Loveland Pass, then back down to I-70. I know it sounds like a lot of freeway, but I-70 actually very nice riding in this area. So run I-70 East to Idaho Springs and take Hwy 103 South. Eventually, you'll come to Hwy 5, this will take you into a State Park where you will ride to the top of Mt. Evans. The parking lot is at 14,260 feet... Don't exert yourself up there or you WILL see spots The ride up and the view is spectacular. Run back down to 103 and head East (becomes Squaw Pass Rd.) You will eventually hit Hwy 74, go North to I-70 and then West back to Old US 6 (Exit 244) and cut back to the East. It hits Hwy 119, Go North. This becomes the Peak to Peak Scenic Highway. Stay on 119 until it becomes Hwy 72 and then take 72 North to Hwy 7. Run 7 North up to Estes Park, and then US 34 West through the Rocky Mountain National Park. Just follow US 34 all the way through the park. Incredible road and views. Watch for roaming wildlife, BIG wildlife US 34 will hit US 40, go West to Hwy 9 and then cut South back to I-70. Dillon or Frisco have places to stay depending on the time of day you get here. From Dillon/Frisco, head South on Hwy 9 to US 285. Run 285 all the way down to US 50 and head West on 50. Run 50 West to Hwy 149. Hwy 149 is another of the really popular roads with the groups I have led in that area, so much so that we have often done it several times on the same trip! Stop in Lake City at Poker Alice's for lunch/dinner. The food is incredible! Somewhere in this trip you might want to stop and take a day off from the bikes. This would be a cool place because you can rent ATV's and run up the East side of Engineer's Pass. Well worth the trip! Anyway, back to the route... Run 149 all the way down through Creede to South Fork. This will take you by the headwaters of the Rio Grande river. About half way to Creede, the road opens up into a big high valley. On your left will be a road for North Fork Creek Waterfalls. VERY cool to check out and only takes about 10-15 minutes. South Fork also has decent places to stay. From South Fork, head West on US 160 back towards Pagosa Springs. Head South on US 84 into New Mexico. Hit US 64 and run East to Taos. Take Hwy 518 South out of Taos to Hwy 75 (go West), then to Hwy 76 (Go SW) all the way down to Hwy 106. Run 106 down to US 285. Then 285 down to Hwy 502 and go West to Hwy 4. Run Hwy 4 West all the way to US 550, then cut South back into Albuquerque. That is the bulk of the really good stuff. I have personally done all of it except for Hwy 76 Southwest of Taos. You would want to layout the mileage and think about where you want to stop each night based on your average daily mileage. When I run tours out there I generally keep the routes to 300 miles per day. However, we don't start until 9:00am each morning and we usually windup at our next day's destination by 6:00pm. With only two riders you could probably do 350-400 miles/day in some place. A lot of those roads are SERIOUSLY twisty so you can't run a 70mph pace Also, the LEO in Colorado don't give a lot of leeway so take care to observe the posted limits. If you have any questions about any particular area in terms of where to stay, things to see, etc,... just let me know. The big problem is that the area where you are going could easily be ridden for weeks on end! I would recommend that you take a day or two off from riding somewhere in all of that. If you are not used to spending back to back long days in the saddle, it can really start to wear you down after 4-5 days in a row. 
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I am leaving on May 8th for 15 days through NM, AZ, UT and CO on my wing!!!! This will be my second time to make this loop, first big trip on bike for my wife. (She is really getting impatient.)
I wish I had realized that before I banged out all the stuff above