In early sobriety working on my recovery and getting my life back on track took most of my time; going to AA, talking to my sponsor, getting my living conditions sorted, getting a new job, etc... After a while, i picked up a lot of hobbies - i didn't stress about doing so, but it just came natural to me as my mind and body got better and i found it easier to focus and enjoy what i am doing.

Now when I am home alone I:
Paint
Read
write poetry
bake
play video games
listen to a lot af awesome AA speaks on youtube
Listen to music
Trying to learn the guitar
watch movies
nature walk
just sitting meditating/thinking (without my mind spinning off into a pit of bad thoughts!)

More social activities I engage in:
AA meetings
Being AA speaker
Fantasy Role Playing
Concerts
Watching sports at the arena
Hanging out with family/friends
Just enjoy walking in the city without feeling like a lost outsider
Going to a cafe
I even happen to get into interesting conversations with strangers about shared interests, which I never did before (apart from drunken nonsense talking at the pub)- for instance at concerts, in the bookstore/role playing store, the cafe, etc..) - it's amazing... last week I was in a "geek" store (they sell role playing games, table top games and the like) - and i ended up staying there for almost 2 hours just talking about games and stuff with the guy working there and a few guys who came into the store... for a guy like me who was always shy (or drunk!) that was a lovely random experience... I used to think i had to drink to be able to socialize - now I just randomly get very interesting conversations with people - and meaningful conversations at that, not just drunken babble :D

In the early days I did anything to keep myself from drinking. I would go to bed at 7PM on Saturdays and watch tv. FreeOwl makes a great point "drinking is the limitation". Its so true.