As with any neighborhood in Cincinnati threre are good blocks and bad blocks. Since you are looking there I assume you must like old houses. There is a lot of restoration going on in the area and there are alot of vacant foreclosures as well. I think the neighborhood is on its way up, over the next 3-5 years The key thing is going to be just who are your neighbors. I would drive around at different times of the day to see what the neighborhood is like. you also may want to check out the CPOP site.
CPOP - Code Enforcement Address Search
Many older homes may have orders against them for repair from the city that WILL NOT show up on a title search, Be sure to check out that site not only for the house you are considering but the ones around it.
You might want to check out the East Price Hill Improvement association website:
Cincinnati's East Price Hill Improvement Association
Also Price Hill Will
Price Hill Will | A Community In Conversation About Its Future
Unfortunately too many people on this board are suburbanites who will tell you awful things about Price Hill and the West side and they've actually never been there. I bought over in Fairmount area (Knox Hill) I am so glad I didnt listen to the naysayers. I have a great house, great neighbors and the area is very safe.