Thanks for your question Bree! Personally, without a car, I wouldn't incur taxi fares and take precious vacation time grocery shopping. We always bring some staples with us such as cereal bars, snack foods etc. For the fresh fruit, you can buy it in small quantities at the resort at Fulton's General Store and the Riverside Mill food court.
If these ideas don't meet your needs, then I recommend
Garden Grocer, an online grocer store that will deliver your order straight to your resort room. Simply fill out the order form before you leave, and your groceries will be delivered to you. It's quick, easy, and from everything I've read and the people I've spoken to, they are a reputable and reliable company.
Have a magical vacation!