I'm not going to be logging time as PIC or gaining any specific training qualification or rating. I could argue it's all sightseeing, but must be very clear that I can't break the rules.
So you don't need a visa or TSA approval. Good.
Don't know about Miami (I guess I would do a sightseeing tour along the Keys and maybe the Everglades) but east of Orlando there's Kennedy Space Center with one of the biggest runways in the world and a few other things that are highly interestesting.
I don't know the specific procedures to get to overfly (and maybe do a few T&Gs) there, but any instructor out there should know.
West of Orlando is Kissimmee, which is home base of Orlando Flight Training, one of the three or four JAA schools in Florida. They operate PA28s, C152s and C172s. Useful if you want to pick up your night rating while over there, for instance. But realistically, if all you want is a bit of sightseeing with an instructor as PIC, you'll find that there are multiple flight schools on virtually every airfield, and any of these would do just fine.
Edited: Just saw Whopities suggestion about seaplanes. I seem to remember some of those at Winter Haven, just a few miles West of Kissimmee too. And there is (was?) a place at Kissimmee that operates P51 Mustangs.