My simple Laundromat plan, based on the fact that I'm a single male traveler.
1. My travel clothing consists of jeans and colored T-Shirts for the outside layer and whites for the inside layer and towels. If someplace requires something dressier than that, I don't go there.
2. I hit the laundry at meal time so I have a better chance of finding two empty washers - one for whites, one for colors.
3. When it comes time for the dryer(s), if several are empty, I'll use a couple of them. Not cheaper, but faster. If there's clothes in a stopped dryer but the window is cold, I'll unload the clothes, dry or not, into a rolling cart and use that dryer. Every dryer I've ever used tells you how much time you get for your dime or quarter. Wear a watch if you don't want other folks handling your clothes.
3. I take a chair, a watch and a book to the Laundromat and sit outside while the machines do their magic.