I've lived in Cleveland my entire life, so let me clear up a few things. First, we didn't actually get that much snow this year. The ski places really took a beating. A normal snow shovel is fine unless you have a mile long driveway.
The city has improved since it got the title, "Mistake on the Lake". We really have had some bum mayors for the last 10 years.
In terms of where to live - it depends on where you will be working. If you are working at CLE, then Berea, Middleburg Heights, and even Strongsville are decent areas. The further out you go, the more expensive the housing. Strongsville is not cheap. Brookpark is kind of questionable. There is a lot of factory housing because of the Ford and GM plants. There are also alot of strip clubs and bars, so it is not the best place for a family. Also, you might want to avoid the near eastside. That is the highest crime area.
For commuting, it is important to be near major highways since just about all of the airports are accessable by them. I-480 is possibly the best thing that Cleveland ever did as is the Jennings Freeway. I live in Cleveland in Old Brooklyn. I am basically as far south as you can go in Cleveland. The community is good and safe, nothing super fancy. I am also right on 480 so I have quick and easy access to anywhere. I can get to Hopkins in 15 minutes or Downtown in 10 minutes. Of course, during rush hour things are slower.
If you let me know where you need to be I can give you more specific information. Really, Cleveland is OK despite what the rest of the country likes to believe. Yes, there is sun in the summer, spring, and fall. It is just the winter that can sometimes drag on. This last one didn't though.
Feel free to PM me if you want more specifics.
Good Luck.