i am fortunate enough that my SO runs a home business...
what do we do together?
well..... my mac is in his office, so whenever i'm online, he's in there with me. we talk about all kinds of stuff throughout the day... mainly current events / world events, and things that he and i see in forums that we go to. we rant to each other about things that piss us off, the amount of stupidity in the world, etc, and discuss between us issues that were brought up in the forums online.
we watch a lot of movies ~ we do the online DVD rental thingy where you sign up and get a couple of movies for as long as you want... you watch them and send them back and they send you more, for a certain amount of $ a month.
we also listen to audiobooks together, then discuss the story, holes in the plot, characters, etc. basically tear apart the story and discuss what we liked, didn't like, what could have been done better, what made the story good (or bad), etc.
once i got out the entire Hitchhiker's Guide to the Galaxy "trilogy" from the local library and he and i would stay up after our son went to bed and read it together. that was so fun!
we go out for walks together (usually to the store, which is the only way i can usually coerce him outside :LOL)...
and we play games (on our LAN)... on very rare occasions we pull out the Chinese Checkers board and stay up together, sharing coffee / tea / beer and playing lots of games of Chinese Checkers in a row.