Don't take a towel at all. No beach towel or bath towel. They take up too much space in your bag. I took a hand towel because it we small and dried quicker.
I later bought a cheap bath towel that I left behind.
There are some places that had bath towels. Wombat Hostels will have bath towels.
In Paris we stayed at The Generator and it didn't have towels.
When it comes to washing, I just put it on to wash and then came back later. I found that other people would just remove your clothing and put it in to a basket so they can used the washer or dryer. If you only have a small amount of washing share with another person you become friends with on the tour.
Pretty much all the clothes I took on the tour I could throw in the dryer.
If you have a small travel hair dryer - take it. From memory there was only one place that had a hair dryer.
Take couple of delicate wash bags with you so that way if someone does take your washing out you wont be flashing your bras and undies to the world plus you wont lose any socks.
A big mistake I made was that I packed too much clothing.
It will be summer so take a couple pairs of shorts, maybe 5 or 6 tops, take a pair of jeans or trackies, a jumper or hoodie, summer dresses too.
Pack a nice dress for if you go and watch a orchestra in Prague like I did.
Make sure you have comfy walking shoes and sandles or thongs/flipfops.
Just remember you can take a small bag on the coach. Have a jumper/hoodie in there as it can get cool on the bus after a while and have snacks and bottled water as well.
I hope this helps.
If you have any other questions please don't hesitate to ask.