If you don't mind a little drive, I'd say you need to eat at the Captain's Tavern. It is near the Dadeland mall in Kendall. Probably the best seafood in Miami.
South Beach - if a little nudity doesn't offend you (topless is allowed), South Beach is okay. Obviously it is quite touristy.
Miami is a big city and with it comes big city crime. If you don't venture off the beaten path you will be okay. The bus service is extensive but I'd stick with taxis myself.