So i can't tell you anything specific to Florida, but i will just explain a few things about watching the premier league in America. Although each game is televised, not every game is aired on a cable channel (NBC. NBC Sports, etc.). That means Leicester's match against Watford (midweek), will likely not be on TV if you go to a bar.
Some of the less popular matches are locked behind a paywall, in a subscription called "NBC Sports Gold." To watch those matches, you have to pay for an annual subscription, and then stream the games online through the NBC Sports App.
Leicester vs Aston Villa (on a Sunday), will likely be televised. This is a good resource to use to determine which channels the games are on in America: https://www.livesoccertv.com/
Just note that the data is usually not completely updated until the week of the matches.
There may not be many Leicester fans in Florida, specifically, but the premier league is popular in every major city. Florida has a large Hispanic population, and they have a MLS team in Orlando (and one soon in Miami), so finding soccer fans should not be difficult. To narrow down a bar, i would look on google maps, facebook, or some of the local subreddits. What you should be looking for is a "soccer bar," or an irish/english pub that opens early enough for the game. If you're staying at a hotel, concierge will probably know where to go.
That's probably not what you were looking for, but I hope that helps!