I'm planning a several week trip to Russia (Moscow and Yekaterinburg specifically) , and I want to pack as lightly as possible --- ideally, I want to be able to do laundry, so I don't have to bring enough clothes for every day of the trip.
On that note: are there laundromats in Russia where tourists can go to do laundry? Or do hotels normally offer a laundry service? If not, are there alternatives? Or do I need to resort to washing clothes by hand in the hotel bathroom?
Laundromats are very rare; I can hardly remember seeing any in my life (actually, I can't remember exactly whether I have seen them, I can just think of some places where they may have been). I guess that if you ask a random person, they will not help you.
There are places where you can drop off your clothes and the next day receive it clean (ask for химчистка khimchistka or прачечная prachechnaya), but the interval differs (some may offer an option for quick cleaning — several hours, — some may require a week), and some may refuse some types of clothing.
At the same time, I think that most hotels and hostels do offer laundry services. However, as always, better check when booking.
Russian apartment almost universally has a washing machine.
This means when you rent an apartment (via AirBnB or even Booking or by googling "квартиры посуточно {city}", the apartment will usually have an operable washing machine and some detergent. If you ask for it in advance you can arrange apartment with washing machine confidently.
So your best bet is sometimes renting an apartment (as opposed to hotels and hostels), making sure that apartment has washing machine, and using it to wash your clothes (note that drying machines are unheard of so you will need to hang clothes on overhead wires or balcony or furniture doors:)
Just google "химчистка золушка" - this is a very common laundry service in Russia.
For example in Sankt-Petersburg - http://zolushkaspb.ru/adress/ ( sorry - only in Russian language, and staff will speaking only in Russian, so be ready for that).
