British people visiting Florida: Target and Walmart are not regular grocery stores or supermarkets. They are big box stores that have added grocery departments. Groceries at Target are expensive and more of a glorified convenience store. Walmart is only a bargain on certain items and usually if you buy in volume. They also don't have a full range of choices like a real supermarket. Having said that, regular supermarkets like Publix, in Florida's tourist areas at least, are pricey but you will have more choices. You need to get away from those areas and try different stores. Maybe find a Piggly Wiggly or similar. However you are probably going to go for what is convenient and close, but that will probably mean paying more. Still much cheaper than eating out.

So excited for you!