Like most of the towns in Mecklenburg county, Matthews is just another leg of Charlotte. If you didn't know any better, you wouldn't know if you were in Charlotte or Matthews. Matthews is part of the Charlotte Meck School system. Matthews has a historic downtown area and a great sports program with MARA. In my opinion, Matthews is a part of southeast Charlotte but of course has it's own police force, town hall, etc.
You can find many neighborhoods in Matthews in very safe areas. What is your price range?