I think it totally depends on what he's into, given his age (I mean he's not like 3 where it's more 'three-year-olds tend to love elmo') - does he like sports? Does he follow a team that you know of? Does he like space stuff, legos, Star Wars, etc.
There are some people with Down's that are lower functioning that will enjoy something tailored toward someone younger but 12 doesn't seem like it'd be so far off unless he's more delayed. I hope you know what I mean - a friend's uncle who had it enjoyed more kid-like stuff than most grown men but as a kid I think kid gifts would have been perfectly appropriate for him.
If you don't want to ask, just think about what you've seen him wearing - team stuff? What you may have seen him playing or heard him talk about with regard to video games, or board games, or stuff like that. Barring that, I'd find another friend with a similarly-aged boy and ask what's in in your area as some stuff is very local, like the marble thing in another poster's area, that kind of thing is not on the radar here at all.