I'm very glad to see so many positive comments about nursing in WDW and public places in general. My slant on it has always been that boobs are there for our babys to be nourished by and people who see that as "dirty" and something to be ashamed of & only done in hidden places, and then turn around an oogle a racey billboard or buy a playboy magazine are just warped! But I do try to always be discreet. I liken it to this: if I had a friend who was a recovering alcoholic, I wouldn't guzzle a beer in front of him out of consideration for him. That's not to say that drinking beer is wrong, just that it's nice to be thoughtfull of others and unfortuanately, some people are still emabarrased at the sight of a mother nursing her baby. That said, I nursed my first 2 boys (age 6mo on one trip and the other age 12 mo on another) all over WDW. Like others have said, the dark rides are the best. Often I had strangers sitting right beside me and they never knew! The moving rides, like Spaceship Earth are the best, bc. the motion and nursing combined puts the baby to sleep. Outside of the rides I'd nurse in restaurants (the only FREE meal in WDW!! LOL) and on benches...just about everywhere. I would try to turn my back to the crowd if possible. I could even nurse walking around when the babies were tiny. You see, I had this big, sturdy bellypack that was always full. It was a great support for the baby's weight!
I know that at certain ages the babies don't like to be covered w/ a blanket and agree that this draws more than usual attention from passersby. I found that a not-so-tight shirt works great. I'd just lift it and withmy free hand hold it so that the material was touching the baby's cheek. Usually the baby then would hold onto my hand and I would stroke his cheek with my pinkie. Most people just thought the baby just had his face up to my clothed chest. In fact I had people come up to me, not knowing that I was nursing, and ask to see the baby. I had to TELL them what I was doing!
Best wishes to all nursing moms out there. To new moms: Stick with it! You will be amazed at how good you get at it after a few months.