I had the same problem, I actually asked someone at my first meeting what he does for fun. I thought it was some big secret, and he was about my age so I asked. His response? "All sorts of **** man". The next night we went to a basketball game (I hate basketball and don't know a damn thing about it but I still had fun).
Tonight I went to a meeting and hung out for a bit and then a bunch of us went to get some food and I laughed until my stomach hurt. I do other stuff that I never used to do like doing laundry, dishes, vacuuming... stuff that I never wanted to do but I knew it was the right thing to do. I find that doing things that normal people do like keeping the house in order will keep my mind busy. I go skiing, take my dog for walks, work on remodeling my house, and go to meetings. Doing "normal" chores also makes me feel like a regular person, and I find that if I see results I feel good.
The real key in the equation of finding stuff to do was going to meetings (for me at least), since I had zero friends and didn't know anyone. There was a point where I didn't even want any friends since I thought I was going to die and didn't see any use for other people. Now I actually have people calling me asking me to go hang out. If I hadn't decided I wanted help, I would have never had the added benefit of getting real friends, who help me stay sober.
It takes time to get aclimated to doing things sober that I used to do drunk. The first few times I felt really anxious and out of place, but the craziest thing was that people around me could tell, and had felt the same way before. They kept asking me if everything was OK, if I needed anything. It blew my mind that they picked up on the fact that I felt weird, and said something about it. This in itself was comforting. Now when I do start to feel uncomfortable, I'll pull someone aside and say "Hey man, I don't know what it is, but I don't feel right". Then I am reminded that this is fairly normal, and my friends will do what they can to help. I am NOT the kind of person who asks for help, but I am learning and it feels good.
This stuff is crazy, I am very grateful to FINALLY know that I am not alone, and even more grateful that I don't have to keep it to myself anymore.