Where are the places that make up the real Cincinnati?

I am attending Miami University and don't have much time left. I love cities of all kinds, and haven't really been into Cincinnati that much. I'd really to know some of the major sights, cool neighborhoods or districts with restaurant recommendations, and any other things you think I should I do in Cinci before I graduate and probably leave the region. The only place I have been to regularly is in Clifton Heights on Ludlow Ave. and the UC neighborhood area. I really like those types of places, so if you can reccomend any other cool offbeat or trendy districts like that, it would be great.