Ditto on all of the posts above that mention the Hungry Bear bathrooms. The one at the theater with Mickey's Magical Map is also pretty good, as long as it's not right after one of the Magical Map shows. Also, right when you enter the park, if you turn right immediately after the tunnel to where the Chase ATM is, that bathroom is usually not crowded and is my go to spot for when I have to go when leaving the park for the day.
The best bathroom in either park though, is the one in Carthay Circle Lounge on the second floor. The doors reach all the way down to the ground so it feels very private in there and I've never had to wait. You don't have to be eating at the restaurant to go and it's nicely air conditioned inside. Plus if you have someone waiting for you, they can enjoy the nice old Hollywood pictures of Walt Disney and jazz standard versions of Disney songs