Cockroach Bay Preserve near Ruskin is a cool place to paddle.
I believe Little Manatee River State Park runs a shuttle if you’re looking for a river paddle. They weren’t running it when we were there in the off season but I saw signs saying they normally do.
For clear water, these are about an hour-ish around Tampa.
I can offer nothing other than be ready for huge crowds on the weekends (and sometimes Fri/Mon).
Some places you have to have make reservations for use and/or parking so strongly suggest going online for current information.
Lithia Springs
Rainbow River Springs
Weeki Wachee
Ichetucknee Springs
Three Sisters
Manateen Springs
Up around Ocala off State Road 40 are two of my favorites, Silver Springs and Juniper Springs run which has a shuttle. Both places rent boats. I think these are more than an hour away but worth the drive. Both are clear water.
I suggest that you paddle through some of our Mangrove Tunnels, It is a really cool experience.
Here a a couple of place for you to check out:
Weedon Island Preserve. Close to Tampa, kayak rentals.
Should go at mid to high tide for the best experience. I have not been there since last years hurricanes so call and check to see if the tunnels are clear
Ted Sperling Park (Lido Key). This is a great place for beginners. I used SRQ rentals for my family visit. The tunnels are well marked and well maintained. ( I was there a couple of weeks ago). It is farter away but very nice.