I assume you mean snorkeling/diving to see fish in their natural habitat. In that case the Amazon really wouldn't be much fun for most people. Dark stain (tannins) and/or turbidity makes visibility near zero in the Amazon and most of its tributaries. This is unfortunately the case in many freshwater locations.
Lake Malawi and Tanganyika, on the other hand, are very clear with great visibility (just watch out for crocs

).
I've never been to Florida, but I've heard it's great!
One of my favorite places to see freshwater fish is the Southeastern Yucatan Peninsula. The cenotes (sinkholes) are full of interesting fish. Some have underground connections to the Caribbean which make for an interesting combo of fresh and saltwater fish. The Yucatan also has the advantage of being very accessible from the U.S.A. (often the cheapest flights to anywhere in Mexico).
What all these locations have in common is limestone. Limestone topography (sometimes called Karst topography) tends to have some of the clearest water anywhere, due to a filtration effect of the fractured limestone, relatively nutrient poor soils, and high pH. You can find clear freshwater in non-Karst areas, but it is always (in my experience) very cold.
This is a cool thread, I would love to see other people's experiences swimming with fish!
I attached a few photos from our last trip to Mexico. This is a place called "el Borbollon" in the mountains of the state of Guerrero. Several thousand gallons per minute of crystal-clear water flows out of the ground at this spot. Unfortunately the only "Monsters" were these tiny Guppy-like (?) fish...
