I was also going to suggest gardening. My dad gave me the book The Square Foot Garden Question and Answer Book (that may not be the exact title), and I love it! Square foot gardening doesn't take up much space, and it yields a ton of produce. I live on a small farm, so I have room for a lot of gardening, but I still prefer the square foot method. I grew so many different things (flowers, herbs, and vegetables) last year!
My sons are 16 and almost 10, and they both helped a bunch, and they loved learning about gardening. They also enjoyed seeing what grew at different times and what grew more quickly. I planted giant sunflowers in the middle of some of my vegetables to provide shade for some of the plants, and my husband suggested we each choose one to see whose would grow to be the tallest by the end of the summer (he enjoyed the garden, too). It was so much fun because one sunflower would be in the lead one week, and then a different one would take the lead. By the end of the summer, they were all taller than my 6'2" husband! Our youngest son won the contest.
Gardening has gotten all of us out of the house more. We spend time together without technology, and we are trying more foods. We're having fun now trying to decide what we want to plant next month.
Another thing we do together is watch Academy Award Winning movies. My husband has collected ALL of them! We watch them together, even the really old ones, and then discuss why we think they won during whatever time period it was. Not all of them are appropriate for our youngest son, but many of them are. Now we also watch all nominated films, but we just started doing that a couple of years ago.
Whatever you end up deciding to do, have a good time! :)