We fly our early, rent a car, have lunch and pick up groceries. We usually arrive at the resort around 3 and room is usually ready. We found we save more money (even with paying for the car) and buying exactly the cheaper groceries we want.
Sign up for Magical Express and let them take the bags to the resort (this way you can rent a smaller car without your bags).
Rent a car from Alamo from the airport (MCOT71) and drop off at the Disney Car Care Center (ORLR72). If you book ahead, you can get a decent size car for $50 for a 24 hour period. I usually return that afternoon.
Bring $1 bills and some quarter. Most major roads around the airport are toll roads. I think you pay 2 x $1.00 and 2 x $.50.
Take the south exit to 417. Follow the signs towards WDW. Take the Orange Blossom Trail exit. After paying $.50 toll, you will be looking at a strip center with an Albertsons (grocery & LIQUOR store). In that same strip center is a Chick Fil A and Ruby Tuesday. There is a Super Target to the right and and a Costco about 5 minutes to the left. When you are done, get back on 417 and follow the signs to WDW.
The Disney Car Care Center is just past the driving gate (where off site people pay to park) to the Magic Kindgom. When you go through the toll plaza, stay as far to the left as possible. You should have a parking pass from your resort, so they will just waive you through. The entrance to the car care center and HESS gas station is to the left. Put in the $5 of gas you burned and return the car. Alamo has a free shuttle back to the resorts & parks. Tip the guy $2.
We have done this a dozen times and it works perfectly.
If you want our standard grocery list, send me a PM.
RR