You can use AAdvantage miles to book air+ground and ground-only packages at the AA vacations web site. And if you have a Citi credit card that is AAdvantage affiliated, you get a 10% discount by going through this link to get the AA vacations:
http://aavacations.com/jp_citidiscount.asp?ref=citi
You also can stack this discount with other Disney discounts, such as the current 7 nights for the price of 4 offering. AA vacations will tell you about these discounts.

There are thousands of possibilities worldwide, of which Disney is a small fraction.

We go to Disney World almost annually, and we alternate using AAdvantage miles to stay at a Disney resort and using Hilton points to stay at either the Doubletree or the Hilton at downtown disney. Also, Hilton has two new resorts effectively within Disney World, on land that somebody refused to sell to Walt Disney way back when.

Not to mention that the downtown disney hotels include a Holiday Inn, and perhaps others that could be booked with points:
http://www.downtowndisneyhotels.com/

Edited to add: of course, the value when using AAdvantage miles to book ground is not great. Even with the 10% Citi discount, it comes to about seven-tenths of a cent per mile. But to me, the trips with my young'n are priceless, and would not happen without use of points and miles. Also, stacking miles with the Citi discount, with 7-for-4 discount at the Grand Floridian -- beyond priceless.