Another place to look for laundry facilities are apartment complexes...I have used them on more than one occasion, was riding through a small town could not find the laundromat, but there was an apartment complex and the laundry was clearly marked
As a general rule I prefer to use a laundromat over hand washing everything. Best touring story: I was coming across the Midwest and a cold front had come through, I was wearing just about everything I had with me and it was laundry day. Pulled into a small town laundromat and picked my machine, put the dirty laundry in that I had with me, then started adding the clothes I was wearing to the load. A lady sitting on the other side was watching with interest as I was peeling off layers.

I stripped all the way down to a t-shirt and a pair of running shorts. She commented later that she was glad to see that I stopped before I hit my birthday suit.
Aaron