There is a Publix north of MK that is close and easy to get to. Navigation systems often do not send you through the non Public area of MK, but as a guest on property you can use it. Turn right (north) out of VGF/GF onto Florida Way. Then turn north on Center Drive from Florida Way and then right on Reams Rd. You actually access the shopping from the off Reams Road instead of Winter Garden Vineland Road. The CM's will also give you instructions to this market. We used it when we stayed at BLT as well as at VGF.
https://www.google.com/maps/dir/28....994,-81.5934579,14z/data=!4m4!4m3!1m0!1m0!3e0
Lakeside Village Center (Store #01396)
7880 Winter Garden Vineland Rd
Windermere, FL 34786-5689
Main: (407) 876-0605
Pharmacy: (407) 876-0417
Liquor Store: (407) 876-0467
I have never take a cab. But you can check with Taxi Fare Finder.
http://www.taxifarefinder.com/main.php?city=Orlando