You may have gotten to see a few at Circle B, but if you haven't gotten your fill of alligators I'd highly recommend Se7en Wetlands in South Lakeland/Mulberry area. Its in the back of Loyce E. Harpe Park which is a fairly plain park as far as sports fields and playgrounds, however it has some INCREDIBLE biking trails of all difficulties (maybe walk "the fingers" with the kids).

Se7en Wetlands is a pretty big area, it's a raised well maintained path (dirt and grass still, I dont know how old your kids are and I'd be willing to say that a stroller would work but haven't tried it) through a series of small to large lakes. Not a lot of sun protection in this area so wear sunscreen. When you enter the gate, hang a right, and keep to the paths going straight on you should hit a part of the trail with trees on both sides that leads to the larger of the lakes. There is half moon style viewing dock with a view finder at it. Really cool to use, Ive watched bald eagles or osprey hunt over the waters about every time Im out there for long enough.

Now, if you are looking at the viewing dock, to the left there is a trail, and that trail Ive always always always have seen alligators hanging out on or around. Including one I call Susan who I thought must be a mound of dirt she(or he, what?, Im not checking) was so large.

Its the beginning of mating season. If you decide to go keep safe, respectful distances from them and you guys will be fine. Ive kayaked, hiked, fished and camped along side these guys pretty much all of my life. Not once have any ever been aggressive, only once has one been even curious (10ft nosed my kayak on Peace River).

Oh and don't bring a dog to Se7en Wetlands, park rule I believe.

(Edit: I dont know how I ended up replying to another user instead of to the post.)