Miami isn't really somewhere you'd want to visit. Miami Beach is where most tourists go. A long strip of beach with lots of big, historic hotels right next to the ocean. There's plenty to look at, good bars and restaurants, and some spectacular buildings. But whether you'd want to spend a week doing that depends on you. North westwards of Miami are the Everglades, nature reserves etc - beside Alligator Alley. Notheastwards are a lot of ritzy beach resorts like Fort Lauderdale. Keep going right to Daytona Beach and Cape Canaveral.
Since you don't want kids' stuff, avoid Orlando. There are lots of Gulf beach resorts like Clearwater as you head north up the west coast.
Depending on when you go, the weather may be a factor. Winter is nice, generally warm and dry. Summer is seriously hot, and humid, with frequent downpours.
Hope this helps.