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.
we always stop at the publix near the outlet mall (off 535/apopka vineland)
Sorry if I missed this but wondering if there is a costco close by? Or SAMs club? We have rented a car and hoping to stop somewhere and buy a few good prepared meals on our way...suggestions?