We've been a couple of times to the south of Florida with our teens - as there are 5 of us, and we're usually on a fairly tight budget, we often stay in suite style hotels. In Fort Lauderdale we stayed at the Embassy Suites - nothing fancy, but comfortable and a great breakfast, with a good pool area, and near to a water taxi stop.
In Miami we stayed in Brickell, which was a good location, near to the Metromover, so easy to get around the financial area and to Bayside Market. If you've got a car, you can easily drive to South Beach, although parking is expensive, or you can get an uber very easily.
It's a simple enough drive over to the Everglades, but I wouldn't really want to do the drive if you're thinking of going to Key West for the day. It's at least 3.5 hours each way if the traffic is ok, and it's usually much longer. Not so bad if you are going to the closer Keys.
Think about splitting your 7 nights, perhaps 4 in Miami/Fort Lauderdale, and 3 in the Keys - we stayed at a Holiday Inn in Marathon - again, simple but comfortable, great pool, nice beaches nearby, and an easier drive down to Key West for the day. Or stay in Key West itself if budget allows.
I know some people aren't keen on Miami, but my teens think it's the best place they've ever been - especially South Beach which they loved. They also loved the Thriller boat ride of Bayside - it's very cheesy, but good fun.