You don't need a visa nor a US licence to do any dual with an instructor on your holidays. You can log all the time against your obtaining your UK licence, simply get the school to stamp/sign your logbook pages as proof.
I can highly recommend
Pelican Flight Training based at North Perry, a short drive north of Miami. If they can't get you a landing at MIA International, then Fort Lauderdale etc make very good second bests.
The school is run by Terry & Meg Fensome, he being a retired Laker captain. Unlike many Florida schools, Pelican are great value for money and completely honest.
I've done a few hours with them in the last year including some low level jaunts along the coastline/South Beach etc. In the USA, the 500' rule doesn't apply over water (ie you can be 10' above the water as long as you are still 500' from any person/vessel etc).