TWA,
You don't know your Cincy geography very well. LUK is on the east side of the city near Mariemount and Mt. Washington. OTR (Over-The-Rhine) is nearly 10 miles from LUK.
J26:
There are new developments and apt rehabs going on in OTR and it's better than it's been in the past 15 years. However, there are still problems there...but, for crying out loud, every city has a "tough" area. The crime rate in District 1 (wherein OTR sits) is actually the lowest in city (News 5, NBC, 3 March 08).
There is affodable, decent housing downtown. The Lamont building on 4th and Central has huge apts, and cheap! I've known several folks who've lived there.
For reasonable living (apt I assume?), you can't afford Mt Adams, Indian Hill or Eden Park. Clifton can be fun--some dicey parts closer to UC (Upper/Lower Clotter, MLKing, etc), but Gas Light Clifton is not quite as "college slum housing" and has neat shops, bars, and theatres on Ludlow Ave.
I'd avoid Western Hills. Hard to get to (really bad traffic), ultra-conservative German family areas-think Rosanne Barr type neighborhoods on crack.
You can find nice apts in Hyde Park, Oakley, Pleasant Ridge, and all will be about 20 mins to LUK. Going east, Beechmont, Mt Washington and even Eastgate isn't bad. Again, like Western Hills, they can be sort of lily-white and boreing...but, like most parts of the CVG area, you're only about 1/2 hr away from most things!
If you want to do the KY side of the River, Covington has good places (closer to the River), but rough ones too...more rough than good. Ft Thomas, and Ft Wright and Ft Mitchell are all pretty golden. I've always liked the old Newport...Dayton, KY is a rare find, too!
Going too far south in KY gets you in "generic subrbia" (Florence, Union, Erlanger) and then you're 30-45 mins from LUK anyway.
There are plenty of things to do in CVG...lots of bars, clubs, restraunts, and hangouts. Theatre (stage/movie) concerts, sports (better summer sports than winter), leagues everywhere, parks, golf courses everywhere, running/hiking/blading/sking trails...Riverbend (outdoor concerts) and horseracing (3 tracks w/i 45 mins) and Riverboat gambling in Rising Sun and Lawrenceburg (45 mins +/-), etc. If you WANT to do something, you can.