Wow, you ask a very good question. There are good areas and not so good areas here in Cleveland, Ohio. The crime you seen based on statistics I have never seen in my 27 yrs of living here. There are just certain areas on the EAST SIDE of cleveland you want to stay away from. Downtown has become a ghost town in recent years, but going down for sporting events, concerts, and even the warehouse district/west 6th street where the nicer bars/restaurants are, would be fine for a single female.
It is really hard to help you without finding out more of what you are looking for. Are you looking to rent/buy??? What price range are you looking to stay in? Based on what you wrote about looking at Westlake.
I will say the two best areas in my opinion for having EVERYTHING at your beckon call would be WESTLAKE AND STRONGSVILLE. They are both within 10-15 away from Downtown Cleveland. Also, if you don't want to spend the high costs of parking downtown you can just take the RTA. Alot of people do that and it is very effective both costly and not having to worry about the traffic every morning.
Shaker Heights is a nice area, but it is on the East Side. Not putting it down by any means, I guess it just depends on if race is a issue or not.
If you want to you can shoot me an email @
jenjeremy040605@hotmail.com, and I'd be more then happy to help you out.