The few residential areas downtown are mostly loft-style, and frankly they’re a little sketchy outside of a few core blocks. I’ve a few friends who have downtown lofts, and love 'em, but visitor parking is an issue, and I wouldn’t go jogging in the area, for example. They also have to schlep to the county to go grocery shopping; not much available downtown.
The city is great for sports fans – not just the professional teams (except basketball), but lots of organized sports leagues. However, unless there is something going on downtown (like a game) the city tends to empty out after-hours.
If you’re not going to live downtown, you need to consider where you’ll live, and what your commute will be like. Most of the really nice areas are in the west county area, along I-40/64 and moving west all the time. Oddly, the most desirable places have French names that no one pronounces as though they were French. If you’ve got kids, you’ll want to be aware of school districts, or look into private schools (very popular in StL) – find a good real estate agent. If no kids, or single, you’ll have a few more options – I’d look near the Central West End, or Clayton (unless you’d like to be closer to work), as they’re closer to the college and just-past-college vibe. More expensive than the 'burbs, of course.
Cost of living is probably comparable to Ohio. As far as I know, real estate is still a buyer’s market, but the area was hit no worse than any other area, so I don’t know that there’ll be amazing bargains.
Quite a bit of the “arts” stuff is near the Central West End/Forest Park area. The symphony is pretty good, the Muny at Forest Park and the Fox in the Central West end have musicals all the time – and the Muny has free seating available at the back every show. There are some local theater groups – like Stages – that occasionally do musicals. There’s also a music scene around the Loop, plus more eclectic stuff at various bars and nightclubs (Central West
End and Laclede’s Landing, plus others I’m too old to be familiar with now).
Good restaurants aplenty – the Hill has fabulous Italian food at every price point.
There are some gems scattered about, but you kind of learn about them by word-of-mouth. Out in the ‘burbs it’s more mainstream chains, with some fabulous local places (e.g., Anne Gunns’ in Chesterfield valley).
Alas, St. Louisians tend to be not great at exercise – game of washers (“warshers”) is about it for most; I’d recommend joining a league or something. Although I’ve friends who regularly jog through Forest Park. Since I find the weather horrid, I just belong to the Y, and work out indoors.
Speaking of horrid weather – if you have allergies, God help you. Pollen and mold counts are usually astronomical, except for a short period in the winter.
Unfortunately, there’s not much in the way of good bookstores. Finding a good Borders or B&N, and ordering from Amazon is about it.
edit to add: for God’s sake, if you’re working on the Missouri side, DO NOT look to live over in Illinois. Cost of living is much cheaper over in IL, and there’s some good bedroom communities, but the commute is horrid going that way. If you’re going the other way – working in IL, living in MO (as I do) – traffic is opposite to that commute.
Try to avoid a commute that requires you to take I-270 for a good way, particularly if it crosses the I-270 interchanges with I-70, I-40/64, or I-44, which jam every rushhour.