I’ve lived in the Columbus area since 1992. The Short North (just north of The Ohio State University on High Street) is where one can encounter a lot of “artsy stuff.” The first Saturday of every month is the Gallery Hop - basically people stroll up and down the Short North as the stores, boutiques, galleries, etc., stay open late.
The Farmer’s Market downtown is a popular locale where one can find ingredients for Thai food (I’m pretty sure, but not entirely). If not there, then definitely somewhere in Columbus.
As mentioned previously, the Drexel Theaters (there are three - the Drexel Grand in the Arena District; Drexel East in Bexley; and Drrexel West in Grandview Heights) all feature independent films. The Wexner Center (on the campus of OSU) tends to feature more “art films” (along the lines of avant guard French or German films, for example) than at the Drexel.
Along with the sports offered by OSU (Columbus is still primarily focused on the Buckeyes), Columbus has two major professional sports teams - the National Hockey League (NHL) Blue Jackets and the Major League Soccer (MLS) Crew. Both are very popular (especially the Blue Jackets), although tickets for the Crew games are easier to get (and cheaper). There’s also the AAA farm team for the New York Yankees (the Columbus Clippers).
As to the best neighborhoods to live in, it depends. If you’re looking to live in Columbus, German and Victorian Village are recent gentrified areas very close to downtown. However, rents tend to be high (you might get lucky to find something nice in the 800-900 range for a small apartment) . Homes also tend toward the expensive side as well (you might be able to find one at a reasonable price if you want a “fixer-upper”).
Other nice areas in Columbus are Grandview Hights - also close to downtown. Rents/home prices are a bit cheaper than German/Victorian Villages, but not by much. A third area is Clintonville, just north of OSU. Not as attractive as the German/Victorian village areas, but you can find some really nice places at reasonable rents/costs. I have a good friend who lives in Clintonville in a nice, quiet residentual area.
You also might want to think about living in one of the many suburbs of Columbus. Bexley and Upper Arlington are closest to downtown and are considered by many to have the nicest homes/places to live (I like Bexley myself but it’s pricey). A newer area is New Albany to the northwest (newer in the sense that a lot of wealthy people have built homes there over the last 10 years; Les Wexner - owner and CEO of The Limited - has his mansion in the area).
Worthington (just north of Columbus) is also nice, but pricey. Just to the West is Dublin and Hililard. I know quite a few people who live in both (home and rent costs are reasonalbe). Likewise for Westerville and Gahanna to the Northeast of Columbus.
You also may want to consider southern Delaware County. Powell, a relatively small community 10-20 years ago, has seen tremendous growth (development in the southwestern and southern sections of Delware County has been especially rapid). The major drawback in living in Southern Delaware County/northern Franklin County is the traffic - I-270 is especially bad during rush-hour.
I recommend not renting/buying a place south of Columbus. True, costs/rents tend to be lower, but all the nice, new shopping areas (Polaris - southern Delaware County; Easton - northeast of Columbus) are to the north.
The job market is relatively good - of course it’s not as good as it used to be what with the downturn in the economy and all; but it’s better than a lot of other places.