If you're not familiar with Florida, perhaps a 'compare and contrast' between 2 relative extremes along the southeast cost would be useful. You can compare my trip report from
Key Largo 2013 to
Jupiter 2014. I'll throw in
this link to a 2017 shark feeding trip (but be aware the owner got bit on the hand and they've had a couple of recent episodes of the boat losing track of divers, though all were found & retrieved).
Key Largo, 20 dives, saw a few reef and nurse sharks. Reef sharks were skittish.
Jupiter 2014, 10 dives, saw a several reef and a few nurse sharks, plus (being the right time of year) a bunch of goliath grouper. Saw 1 roughly 5-6 foot shark, likely a black-trip but maybe a sand bar (at a distance & it didn't stick around).
Jupiter 2017, 7 shark feed divers, saw 3 tiger sharks, 2 silky sharks, some nurse sharks, more lemon and bull sharks than I could keep up with, some goliath grouper.
If you want to reliably see fairly big sharks without feeding, I suggest one of 2 options if you're aiming for the U.S.A. - either hit Jupiter, Florida during the lemon shark migration, or try the off-shore wrecks out of North Carolina (
trip report) where you can get close action with sand tiger sharks. August is likely to be a good time for North Carolina...
Richard.