What part of Florida are you going to? Its quite a diverse state, and like anywhere on the planet, it has its negative stereotypes - but overall I'd say Florida is a pretty sweet place to visit.
Yes, the weather can be a bit temperamental - super hot and humid one minute, hurricane coming through the next... But if you're coming from England, you'll probably can't complain about the weather.
Regarding things to do; the obvious ones are Disney, Universal, Sea World, boating, scuba, snorkelling, or just hanging out at the beach all day...
And about the accent thing, I can tell you it will definitely help create an "air of mystery" about you.
I had the reverse experience, rocking up to boarding school in the UK with an American accent, and you do get attention for being different from everyone else.
How you use that attention is down to you I guess!