This is what I have read for AAA room only discounts:
Value Season: 15% off Value, Deluxe & DVC
20% off Moderate & FW
Regular Season: 10% off Deluxe & DVC
10-15% off Value, Moderate, FW
Peak/Summer Season: 10% off all resorts
Holiday Seasons: Blacked out
FYI, Travel agents can also book your AAA room only discount, even if they are not with AAA.
If you want to go during the FREE DINING promo...
For the most part, if you're staying at a value, the discounted room & ticket prices won't compare to the food savings if booking rack rates and full priced tickets.
Really... say the room is $100 rack rate (pretty close estimate for value season in a preferred room... round numbers are easiest to work with here) and Disney gives you $15 off per night for AAA. (Going by the info given by ncdisneygal... thank you!)
Each ticket, you might save $2-3 per person per day. (Maybe $10 total per day.)
If you're a family of 4, you might save a total of $25 per day doing these separately bought pieces ($15 room savings + $10 ticket savings)...
Chances are that you won't feed your family of 4 for a full day for $25, unless you get by on water and smuggled in bags of cereal... Even just one CS meal for such a family is going to be more than that $25.
The AAA savings might be worth while if you intend to stay at higher level resorts, however.
If you stay at the Polynesian with a rack rate of $355/nt, you'd save $53 for the room for the night, plus your $10 for tickets, meaning you have $63 in savings to spend on food... this still cuts it close to plan $63 for a family of 4 for meals for a day, but it is possible with some creativity. I just think that if you're going to be that frugal with your funds, you probably wouldn't be staying at the Polynesian in the first place!
It really comes down to this: how much do you budget for meals for your family for one whole day in Disney?