You don't even need a laundromat. All you need are high-tech quick-drying fabrics, a small bottle of liquid laundry detergent, and a sink. I wash everything in the sink as soon as I get to my daily destination, wring it out, and hang it up to dry. By the next morning, everything is generally clean, dry, and ready wear again.

For stuff that's critical (ex: cycling shorts) I'll bring an extra to use if the first one is still a bit damp come morning. In general, I try not to bring more than 2 of any piece of clothing.