L.Z.
If it's not too far for you, Land O Lakes Public Library has story time for toddlers. It's free. You can check it out at http://pascolibraries.org/ or perhaps there's a public library closer to you.
Also, on SR 41 in the Winn Dixie shopping center, there's Planet Bounce. It's a bounce house that has those inflatables and a toddler area for kids to play indoors. It's $8 for 2 and up and $6 for under 2, I think...http://planetbounceparty.com/owners.html.
When it's not raining, there are all sorts of wonderful free parks/rec centers - Land O Lakes on Collier, Lake Park on North Dale Mabry...
Another place my daughter loves to go to is the pet store. There's a great one on North Dale Mabry, Petland. You can actually handle the pets they have - dogs, cats, hamsters, birds, etc.
Barnes and Nobles also has a free storytime. You can go to their website to find a location nearest to you.
Hope that sparks some ideas....have fun!