Are these three-way switches?
One red wire on one screw, right? And two black wires under the other screw (or poked into those dang quick-connect holes I hate so much)? If so, that's an ordinary switch, not a three-way. If it actually has three screws on the body of the switch, though, it's a three-way... and given your description of things, there's no really good reason for that.

If indeed you have a red wire "going to one location" and two black wires "going to another location", then ONE of those black wires should be the power feed and the other should be power continuing on to the next switch ON THAT FLOOR, unswitched, so as to supply power to the next lighting area. The red wire should be the one headed to the light fixture.

Might not be, though. Sparky guys wire all sorts of things in different (often incorrect) ways, so if you run into an ambiguity it's Best To Test.

To verify my suspicions, could you post a quick photo of the wire connections to that first switch?