Hi Margaret!
Not having a car while staying at a Walt Disney World resort hotel is not a problem at all!
Disney's Old Key West resort and
Disney's Saratoga Springs Resort & Spa are both located within the Downtown Disney Area. Both have excellent bus transportation provided to all of Disney's parks & waterparks as well as a ferry that operates along the waterway to the
Downtown Disney Area.
As far as distances to the parks and shopping areas are concerned, Old Key West is perhaps very slightly closer to the parks than Saratoga Springs; while Saratoga Springs is slightly closer to Downtown Disney than Old Key West; however, both are very similarly situated on the Walt Disney World property as a whole. Have a look at the pool areas, room decor, dining options & extra amenities offered at both resorts by visiting their information pages linked above, to see which seems to fit your personal tastes the best!
If the ability to pick up groceries for use in your Villa accommodation is of concern without a car, you'll be please to know that both resorts are quite well stocked with most amenities you'll need right within the Artist's Palette eatery, grocery & market at Saratoga Springs or Conch Flats General Store at Old Key West.
Using GardenGrocer.com, a non-Disney-affiliated local grocer, is also an excellent way to ensure that you're able to receive all of the grocery items you need without a vehicle. You can place your order with them in advance of your vacation and have it delivered right to your Villa!
Wishing you all the best for a Magical vacation Margaret!
Kirsten