The restrooms are pretty unpleasant in some cases, but I don't care to breastfeed my child in public, either. If I absolutely had to nurse, my best recourse was to go to the nicest (cleanest) department store, grab an article of clothing, and head for a dressing room. Sometimes those are pretty nice, roomy, and depending on the layout, can be very convenient for nursing.
Bingo! The dressing rooms are excellent and for that purpose. Some are even dim enough that a little shut-eye with feet up restoreth the soul, while nursing a wee one.