We visited the Tampa Zoo last Nov. It is a cute zoo...we're zoo members so it was free. I thought the regular tix prices were a bit high.
We're members of our local zoo, which is reciprocal with both the Tampa and the Central Florida zoo, so if you're not zoo members you might see what the local zoo charges for memberships and if they're reciprocal. We've got five kids, so memberships often make more sense for us than buying tickets, but if you've only got two kids and travel a bit the zoo card can end up paying for itself as well.
The "beach hunter" site has reviews of many Florida beaches and I know there's a nice one in Cocoa beach that has a (shaded) nature trail that sounded good to me (Lori Wilson park). There's also a little Astronaut memorial there that might be a nice break in the heat of the day (Astronaut Memorial Planetarium and Observatory). Not far from Cocoa Beach is Melbourne, with the Brevard Zoo, which gets terrific reviews. Cocoa Beach and Daytona Beach are closer than Tampa, but some people much prefer the Gulf to the Atlantic.
There's a science center in Orlando proper, that might be worth checking out if you have a membership that'll get you in for free, but it gets mixed reviews so I wouldn't go if you have to pay full price. The Henry P. Leu Gardens should have a ton of stuff in bloom around then, and there's a free half-day once a week, Monday mornings I think, which would be good if your four year old is okay with that sort of thing. What I'd love to do is the Tiffany exhibit at the Charles Morse Museum, but there aren't many 4 yos who'd like that.
Some friends of ours spend their "off day" checking out the biggest McDonald's in the world and doing Downtown Disney - the
Lego store in particular. Which wouldn't be a non-Disney day in my book, but whatever. Oh, and Farris and Foster's has Chocolate making nights, where you buy a pound of chocolate you can make however you want - mold or mix or dip or whatnot. I think family night is Monday, but check their website.