I've lived in the area my whole life.....if I were buying in this area it would be anywhere except Lorain and Sheffield Lake. Lorain is on a down swing.....losing (lost) most of the good, base jobs and Sheffield Lake has never had any.
Be aware of the all the different "Sheffields" and "Avons" too. There's Avon, Avon Lake, Sheffield, Sheffield Lake and Sheffield Township.
Avon Lake and Amherst are probably your best bets for schools (west of the Cleveland suburbs) and, as far as I know, two of the nicest city type communities to live in in the area. Most of the stuff between Avon Lake and Cleveland are nice too.....Bay Village, Rocky River, Lakewood, Westlake, Fairview Park, etc. Sheffield Village is OK but the schools aren't the greatest (Sheffield-Sheffield Lake school system).
Just like anywhere else, there are good and bad to all cities.
I too would recommend getting to know the area before buying.