like everyone else has said just find a quiet place off to the side in any of the parks and you should be good. never got any bad looks from anyone just smiles from some moms which was nice and comforting for me since it was my first child to be doing this at the parks with i was quite nervous. he was 9 months at the time so he was able to go a little longer between feedings which helped also.
funny story i have about one incident though..we were eating at O'hana for dinner. he wasn't quite having it that night was a little fussy. my husband took him out to feed him some baby food by the bar area since he was getting restless at the table. he ate the whole big jar but wanted more. we had an awesome table at the front of the restaurant by the windows for the fireworks too. he came back with him still fussing and hungry so i am like ok i'll feed him and thankfully i had my cover up. well i wasn't paying attention to the time and i had my back to the window and just as i put him on...the lights dim and everyone in the restaurant turns their chairs to watch the fireworks. now i know they weren't looking at me.

the fireworks are the main attraction but it was still very embarrassing for me because it was towards the beginning of our trip and i was still getting used to bf in a very large public place. but i just acted normal and went with it and it kinda helped me get more comfortable doing it around the parks more.
the baby centers do have nursing rooms but i never was close to use them. plenty of places to do it between rides and shows

have fun!