I have found that my oldest daughter, Sarah (12), likes to go fishing at the pond across the street. Actually catching anything is just a bonus for either of us. She really just wants alone time with me away from the other two. It is also a time when she is likely to casually bring up some topic that may be on her mind. So if she asks me to go fishing, I try as hard as I can to make it happen.
Daniel is the middle kid (10). He just wants to play. He'll ride the GS with me, dirt bikes in the yard with me, basketball in the drive way, wrestling anywhere, climbing MUCH higher in any tree than I would ever attempt, watching any moto or nerd engineering related video on YouTube we can find, fishing at the pond, etc,... But he's not a deep talker like Sarah. He's ALL energy!
Rachel is the youngest (8). She desperately wants to ride on the GS because "it's not fair" that the other two get too and she doesn't! That tends to be her reason for doing many things
She'll toss around the basketball with me, ride dirt bikes in the yard, and snuggle on the couch for a movie or to read a book. EVERY time we are in the garage, she wants to sit on the GS to see if her feet reach the pegs yet.
All three like sitting in front of the computer with me watching cool vids on YouTube about all kinds of stuff. We enjoy the Smarter Every Day series. They love the Slo Mo Guys. We've watched just about every video there is about how things are made. We've seen uncountable buildings imploded. We've watched videos on chemistry, physics, astronomy, a live feed of the sun from some NASA solar observatory satellite (very cool), documentaries on plate tectonics and volcanoes, CNC machining, metals testing, mining operations, rockets launching, and much much more. I will often pause the videos and we'll discuss the topics or particular issues about the videos. The cool thing is that they don't think of this as "school" (we home school). They think of it as goofing off, so they are more in to it and interested, hence they tend to pay attention and retain well. It is really neat when we are out doing something else and something happens that triggers a memory of some video we watched and they start relating the topic of a video to what we are doing and it is totally relevant! It is also neat to see them making connections between various fields and topics by seeing underlying principles and concepts, and then thinking about how they might apply to other situations. Sometimes we might sit at the computer in my office to do this and other times we are all in the living room watching stuff on the big screen TV that is hooked up to a PC. I really enjoy this time with them.
Lastly, and this might offend some people (although I don't know why...), we end each day as a family sitting in the living room praying together. It is time spent talking about people outside our family that are having struggles or which may have had good experiences. We talk about issues the kids might be struggling with, friends, school work, each other, and even with us. We look for things for which we should be thankful. We encourage them to think about areas of their behaviors and attitudes that might need improvement. We talk about the need to forgive people that they think might have wronged/offended them. Then each person gets time to pray, without comments from others during or after, and then they go to bed. It doesn't sound exciting, but we have tried to keep this going since they were very little and hope to keep it going as long as we can keep them doing it. It is a great way to keep your finger on the emotional pulse of your kids and the family as a whole. It is serious quality time! We include their friends whenever they do sleep overs. I'm guessing the kids like it as well because they are always bringing up things to remember for later in the evening and they are good at reminding me if I forget someone we happen to have been praying for (like numerous TWT folks over the years).
Another thing they like is being able to go to town with me or my wife without the other two kids coming along. Every morning one of them goes with my wife when she goes to the gym. If I have to make a Home Depot run they usually fight about who gets to go with me. Sometimes, one of them will get to come to work with me. I am self employed and work with my Dad at their property so they get to see my folks as well.
Really it boils down to one issue. They want to know they are important to us. More than anything, spending time with them, doing almost anything, makes them feel that they are important. The quality of the time spend is important, but you can't use it as a substitute for quantity. They are smart enough to know when I simply cannot spend time with them, like if I have to work, and they know when I make a choice to either spend time with them or not. They are also smart enough to know that there are times when I need to be able to NOT spend time with them simply because I need some alone time. So, like anything else in life, it is a constant struggle to juggle all the competing issues and maintain a good balance. I think this it is important for them to see this and to learn how to do it in their own lives.