Went to two or three meetings a day when I first got sober. I needed all the help I could get, and I don't do sitting still well either. No Internet back then. Living in NYC makes it easy to find things to do, but you might be surprised at how many people never leave their apartments.
Didn't spend much time thinking about what I'd do, just did it. Running, martial arts, preparing for grad school, AA softball team and then softball team from work...anything people asked me to do that didn't involve alcohol. Helped friends move, sat in on classes at the Arts Students League, movies, hanging out in Central Park, the Cloisters, art museums, motion picture museum, lectures, Lincoln Center, Empire State Building, dinner with new friends, visiting my family on Sundays, volunteer work.
If I had enough time to think about what I was going to do, I'd often think myself out of doing it.