Are you staying at BLT? If so, there's a publix out the "back gate" of MK -- turn right out of BLT parking lot, take a right at the first stop sign, then another right at the "T". Follow that road on around and you'll get to a traffic circle, which you should exit as if you were going straight through and there were no traffic circle. Publix will be up on the right. It takes about 5-7 minutes to get there from BLT.