I'd plan to stay a few nights in two or three locations, Key Largo, Middle Keys and Key West.
I might add Florida City/Homestead for a night or two for a visit to the Everglades NP. It's mainly budget motels there, but being right at the end of the toll road would be a good place to stop and rest, especially if you have arrived after along flight early evening (which will seem much later).
I like the hotels around MM100 (mile marker 100) such as the Holiday Inn but there are several resort properties to choose from. Not sure what your budget is. There are plenty of restaurants though they are more spaced out in the Upper or Middle Keys which may necessitate driving to get s choice.
In terms of what to do, apart from lazing around it's mainly water based activities like snorkelling, diving, boating fishing etc. along with various wildlife activities. Key West offers plenty of bars and nightlife.