I like Miami but as stated its not a relaxing place. Crazy traffic, not as bad a NYC but I think all the taxi drivers are from there as they drive around honking their horns for no reason. South Beach is the "in" place to be. If you decide you are going there stay on South Beach. You can walk to Lincoln Mall, visit Biscayne Bay, take one of the Miami water tours of the homes of the rich and famous and see art museums, etc. South Beach is where the pretty hotels and clubs are located which is what you see on TV. Not every bar is a club and there are good restaurants and art museums, etc. If you have 4 nights I would spend 1 or 2 in Miami then a couple nights in the upper keys as suggested. Not quite Hawaii but pretty and relaxing. You can make a day trip from there to Key West if you want to visit the "Southern Most Point" or just stay in Key West if you want more to see and do in one location.
Check out the Miami and South Beach forums to see if its what you really want to do. And the Florida Keys And Key West forums too.