All, thanks for the great suggestions, story so far:

Options to wash/dry fast drying synth clothes:

Ideal

1) Wash and dry using motel or other laundry in town. Use down time to rest/eat/socialize/shop etc

Other options

1) Wash in basin

2) Squeeze out as much moisture as possible, wrap in towel/synth chamois to sponge out more moisture - extras: stomp on towel

3) Dry using clothesline outside the room

4) Dry using clothesline in bathroom, run the fan

5) Dry using heat source such as lamp, hair dryer

6) take a couple of spare hangers

7) take a mesh bag to dry in the bag of bike (outside pannier, not inside)

8) Probably not so great option for people who prefer dry clothes: Wear if still damp and dry while riding the next day, its getting wet anyway.

Stuff to take: clothesline, synthetic towel/chamois, mesh bag, bungee cords, plastic hangers