Grandview Heights is really a cool little town - awesome little place to live. It's quiet and shady and very walkable with tons of awesome little places to eat and drink and a great social scene a little older in age than the drunken Ohio State kids. Several new condos have been built that are very expensive. Depending on what street you're on, you have a beautiful view of the downtown skyscrapers and the 4th of July fireworks. Not sure on home prices, check zillow.com and search the 43212 zipcode. I've lived in a cool house here (split into 4 apts) with gorgeous wood floors, arched ceilings, fireplace, and tons of character. There are duplexes as well.
Clintonville is nice too, although it's not as cozy or as intimate as Grandview. Traffic on High St. is a royal pain. I have many friends who own beautiful homes there so maybe it's a little more affordable than G'View. Some of the streets north and east are rough. Due south is the northern reaches of Ohio State's off-campus madness.
Victorian Village is also lovely - beautiful old victorian homes with many split into duplexes. I've lived in a breathtaking Victorian duplex here. The Neil Ave region of VV is much nicer, safer, and quieter than the High St side.
Upper Arlington is also an option - this burb is just north of GView. Lots of beautiful homes, condos, and apartments. Very family-friendly. Lots of young couples walking their dogs and strollers. The part of UA south of Lane Ave is extremely fancy; the part of UA north of Lane Ave to Bethel/Henderson is more for normal people.

I've lived here as well.
In terms of snagging a place to live, I found my GView, VV, and UA places by just driving around - tons of signs advertising. My GView place was run by Kohr Royer Griffith - huge but awesome property management group. You can search for places on their website here:
Kohr Royer Griffith Inc.
You'd also might like German Village or Bexley but I didn't spend enough time there to give you info.