The only hotels I know of that have self-service laundry room (tokens available at front desk) are the Holiday Inn Express chain. Holiday Inn Express Dongzhimen might fit the bill....it is about 15 minute walk from the Dongzhimen subway/Transport hub though. Another option is to book the hotel you want on the central or near northeast side, and use this company, started by an American fed up with overpriced hotel and overpriced/slow Chinese chains: https://www.laundrytown.com/laundry-beijing/