What are the rules with regards to landing a float plane on a body of water? Can I land anywhere (non-emergency, obviously) that would also accommodate the take-off? If not, how do I determine which bodies of water would allow it and which would not?
It really depends on the state, though you can't land in National Parks (the National Park Service regulates that, not the FAA). The FAA doesn't care where you land it, though if you ball it up due to poor choice of landing area then they'll have something to say.
Some states don't really care where you land (like Oregon), others don't let you land anywhere (like New Jersey). You should contact your state and get the regulations from them.
This is handled on jurisdiction by jurisdiction basis. While sea plane "bases" are marked on the sectional, this only means that the location has been registered with the FAA.
The air space over the water is handled federally. The water itself is handled locally. When the aircraft is on the water, it is generally considered a boat under the law, except where a jurisdiction has chosen to single out sea planes.
Unfortunately many jurisdictions have done just that. Any little mud puddle can potentially be banned for sea plane operations by the local community.
There is an association of sea plane pilots who involve themselves in advocacy to keep waters available. They publish some useful materials on this subject.
If you plan on going for your sea plane endorsement, your instructor will give you the pertinent details. If you would like to fly locally, you will need to check out your local codes. If operations have not yet been banned, it would be sensible to join the association, and take an active role in keeping local waters open to sea planes in your area.
Drawing on some personal observations, many float-plane sites around Seattle are marked on maps.
But I've also observed float planes taking off and landing at sites that are not appropriately marked on the map.
I cannot cite regulations, but my eyeballs suggest that any safe place may be legally okay.