I don't know which hotel you're staying at therefore how close you'll actually be to the Resort, but we found a massive one on Chapman which is great - we've used it both times we've been now. We find it easier to go to the laundromat and get it all done in one instead of waiting for one of the machines to free-up back at the hotel.
It's a bit of a way from the DLR and others will probably know of ones closer to the Resort but no matter what, we'll stick with this one.
From the Resort, come out of the main gates and turn right onto Harbor. Keep going 'til you reach Chapman then make a left. It's in the first block (a couple of stores down) of shops.