Thanks everyone. The holes have been on the outside rim, so I suspect it's similar to skilsaw's son, and I am getting flats from dirty parts of the road shoulder. I have been keeping the tires fully inflated (even though 120 psi seems crazy to me; that's what the outside of the tire says....)

If they are around $80 for two and they'd reduce the number of flats, getting the Bontrager hardcase or Specialized armadillo tires would seem to make sense for me. If anyone has thoughts on what kind of tires with a kevlar belt are best, I'd appreciate the input.