you can rent a fridge for your room for I think $10/day. There is a mini-bar in the room, but I don't think they like you taking their stuff out and putting yours in. I kept a cooler in the room which I filled with ice every day for drinks. I did get a quart of milk and was able to fit that in the mini bar with their stuff.
I don't know about a grocery store close. We went to super target which was just a little ways up I-4 at the next exit past Florida Turnpike it was right off I-4. I got our pop, milk, cereal , snacks, and water there. Just as cheap as the target at home. Didn't take more than a few minutes to get there.
