If you know any expats, ask. Hotel concierges check. The hotels will say they do laundry, but then look at them, smile and say, that's far too expensive (this tactic works better when in Mandarin). Usually they'll smile and give you a heads up. If you write "Forenet" its a chain, they might know.
There's a Fornet or two on Xinjiekou Wai street, near where I used to live near xiao xi tian. I know they do pressing and dry cleaning, and am sure they could do laundry too. If you're coming from a most eastern part of town, take a right onto Xin Jie Kou, if you're coming from a more western part of town on the second ring, make a left onto Xinjiekou. Drive along XinvJie Kou for 300+ yards and there should be a Forenet on your right side, the sign will be in a blueish green and "Forenet" will be written in English.
洗衣 - are the characters you want to look for otherwise.