Re: Light switch to no where? 3-way switch with no other end?
It's very hard to say what it could be to. Typically, the first switch in a series (closest to the door ) will operate the lights in that room, subsequent switches will operate exterior and additional lighting. Your switch probably used to control the room at the back door or as you suspect, the kitchen, and could have been abandoned during a remodel OR the previous owner didn't know how to hook up a 3-way switch when one failed, leaving this switch inoperable.
I would get a book such as "Wiring Simplified" that will show you how a 3-way circuit is wired and you can start tracing nearby rooms/lights for signs that a switch was replaced improperly. If you're not comfortable doing electrical work, call an electrician. BTW, never work on a live circuit. While the power will need to be on during some of the diagnostics, turn it off at the breaker before messing with the switches and wires themselves.
My guess is, you're either going to find it wired improperly, or you'll find a single pole switch in place of where a 3-way should have been.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!