We just stayed there this summer.......from what I recall, there is a grocery store right on Central Florida Parkway - near SeaWorld. I am guessing that since you are driving from the airport that you will probably take the Beeline to John Young Pkwy. I don't know what is down that way - we only travelled towards I 4. If you leave the hotel and head out on Central Florida Parkway towards I-4, there is a ton of stuff....Wendy's, etc, and grocery store. Can't miss it...it will be on your LEFT heading from hotel towards I-4.
Have you been to this hotel before ? WOW !! What a place ! Feel free to contact me if I can help you further !