Tavern on the Bay near downtown should be a good place to watch the game. Waitresses wear yoga pants. Lots of TVs. BBQ Pork Nachos are good there.
There is a new smaller place in East Naples called Tacos and Tequila. Great food. One of the owners is a LSU fan. Tell the owners/managers you are an LSU fan. They should be able to set you up.
There are also a couple of Pelican Larry's in the area. Good wings. Cheapest beer in town.