In the 80's, urban flight left downtown Cleveland in trouble. The town has done much towards rebuilding the area such as with a relatively new baseball stadium and warehouse district with restaurants and bars. Nonetheless, there is still remnants of urban problems and so there are homeless and the like downtown. I guess every city has this to some extent. Tower City seems to attract all sorts and so be mindful not to stray too far from your destinations.
Driving in Cleveland is a drag as main roads often have a speed limit of 35 miles per hour with some areas changing to 25 miles per hour. One road, Mayfield, runs from Case Western to the suburbs and has such changes (i.e. speed traps). This is par for the course in old cleveland. One needs to pay attention to the posted speed limits. Also, in some places there are traffic lights every 1/8th of a mile so sometimes its slow going. (Hm. It's said Cleveland's economy is sluggish - wonder if it has anything to do with their outdated traffic system!!!)
The only neighborhoods considered dangerous are those tourists have no reason to visit. There are many panhandlers downtown, but they are harmless. Enjoy your stay in Cleveland! :)