Parking is $8 per day per passenger vehicle (noticed that yesterday when we were there).
Even tho AAA may throw in "free" parking there is no special designated area for AAA parking. You park with the rest of the mob, possibly in the corner furthest from the escalator that will take you to the tram (no way to guess where you'll end up parking based on time of day you arrive, sorry).
Driving versus shuttle -- I would tend to prefer the shutttle personally ... BUT ... would want verification from the hotel as to how often it picks up / drops off. If the hotel is using the new Anaheim Resort Transporation (ART) system as their shuttle, pick up / drop off times should be roughly every 10 minutes. Not shabby. But definitely confirm first with the hotel. You don't want to be stuck to a shuttle schedule that only leaves the hotel on the hour and leaves the park on the 1/2 hour.
Another question to ask: if using the shuttle (or ART) what is the estimated "travel time"? For example, do you leave the hotel at 8 AM but get to the park 45 minutes later because the shuttle stops at 13 more hotels on the way? Or is your hotel at the end of the long list of pick ups in which case you may not have any seats left!! If so, drive yourself! If they shuttle/ART travel time is 10-15 minutes, you might want to consider it then.
Think of how long it'll take to drive from the hotel to the parking garage, wait in line to enter the parking garagae, possibly park where you might have to hoof it just to get to the tram (and then hoof it back after getting off the tram when you return to the parking garage), then the time it takes to get back to the hotel.
Will you have a car with you anyway? If so, I'd suggest trying the shuttle/ART route first. If it doesn't suit your needs, then try driving to see if that works out better.
