It'd be wise to avoid the near east & west side areas of downtown Cleveland. Although there's history in many of those neighborhoods, you'd be best to simply drive through, instead of walking around. The west side is safer, but I'd never leave your car while in the east side, especially at night.
If you are tooling around downtown Cleveland on game day, beware. There is no driving etiquette...whether you are walking or driving BE CAUTIOUS!! If you are using the rapid to get downtown, they become VERY crowded on gameday. If you are going to the Great Lakes Science Center or Rock and Roll Hall of Fame when there is a Browns game, parking will be a nightmare as the football stadium is right next to both of these places....the crowds will probably be a bigger nightmare.
Baseball Games are played at Jacob's Field, more toward the center of town. The ball park is surrounded by nightlife....so if you are going out around the Jake, don't do it on gameday!!!!
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 It's said Cleveland's economy is sluggish - wonder if it has anything to do with their outdated traffic system!!!)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 Flats, a nightclub area at the mouth of the Cuyahoga River downtown tends to get a bit raucous, so be careful. Just about all the crimes are alcohol related. Bar fights are not uncommon, or drownings of drunken boys trying to swim across the river to the West Bank and the meanest bouncers you ever did meet. The police however, keep the place in pretty good check and the crime rate has diminished significantly. A couple of summers ago, a sports journalist from ESPN decided to take a whiz from the 2nd story window of a Flats bar called Have A Nice Day Cafe. Fate would have it that he pissed right on a cop standing on the sidewalk down below. Needless to say, the police officer was not amused. The talking head was so busted !!!!
So if you are in the flats and do something foolish in the heat of the moment and find yourself perp walking to a cell at police headquarters, call my friend Phil. He will tidy up your life for you.
I can't say that there are any unique dangers that are specific to Cleveland. One should use general precautions, as you would in any 'big city.' But I think, for the most part, Cleveland is pretty safe. I did find myself stranded in a seedier part of downtown once, and that wasn't the best feeling in the world, but the police were patrolling fairly frequently, and I made it home in one piece!
Well, Cleveland is a relativly safe place. Take the same precautions you would anywhere. Drivers here are not the best, but it is better than many oher places I have been. Do beware of the slick winter driving conditions. Also, beware of the many panhandlers downtown. They are mostly harmless, but very aggressive in their tactics at times.
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! :)