I found the hole where they're coming up from the (unoccupied) basement into our kitchen coat closet, and cleaned up a whole bunch of mouse poop in there, but I figure they'll be back.
I went to Home Depot and got a live trap (employee: "If you're having trouble deciding, I recommend the Predator spring traps." "No, I'm looking for a live trap." "A live trap?" "I'm not much of a predator.")
The trap I got curiously promises to catch "up to 4 mice" (the fifth one lines up outside, and so on), so in the morning hopefully the smell of organic, no-preservatives peanut butter will have worked well enough to catch, say, one.
And then I will figure out what to do with my live-trapped mouse.
(nyxie says I can't keep them as pets.)