Go over the Winter Haven, the Indians practice is more "open" to the public, hours before every game. Plus, it's easy to sneak your own beers into the Indians outfield picnic area.
The Big Bamboo, closed by hurricane damage, has now been burned by bums sleeping there, so go by there and have a brown bag in the parking lot.
Golfing is always an option, plenty of relatively cheap public courses all around.
We're hoping to be there the weekend of the 17-19th. God-willing, I'll be carrying around our 1 month old Astro fan.