You might want to read this blog before fishing in TV.
The Villages Best Fishin' Holes
Most any fresh water in Florida will have gators, and just having people around doesn't deter them, if you play golf you'll know what I mean. They are out sunning themselves on the banks quite a lot. I would fish at Lake Miona Park off Rainey Trail. It has a dock, restrooms, picnic tables, etc. I'm not sure if you need a license, see the two links I provide.
Lake Miona Park | Sumter County, FL - Official Website