Nursing is legal in California thanks to California Civil Code 43.3. Edit: As of July 2018 breastfeeding in public is now legal in all 50 states! That means that you may freely breastfeed your baby anywhere at the Disneyland Resort! Each park has a fabulous baby center where you can pick up anything you may have forgotten, formula, bottles, diapers, wipes, baby Tylenol, etc. You can also nurse here, heat up bottles and baby food, wash bottles or utensils in a clean sink with dish soap (yay!) and even feed your baby in a clean high chair. It is air conditioned as well and you can rest here whenever you or your baby need to.
The only downside to this is that there is only one baby center in each park, so that means if you chose to nurse here you would be trekking over from wherever you were in the park multiple times a day. I don't know about you but I have no time to waste while at the parks and would much rather line up feeding times with nursing friendly rides and experiences.
These are my favorite places to nurse at the Disneyland Resort. Some even double as great places to bring a napping baby!
The Disneyland Story Presenting Great Moments with Mr Lincoln
Star Wars Exhibit
"it's a small world"
Pirates of the Carribean
The Enchanted Tiki Room
Any shaded bench or restaurant seating area
Disney's California Adventure
Turtle Talk with Crush