25 minutes?!??! Not hardly.
There is a very nice Publix two minutes away. Take Sea Harbor to Westwood Blvd. (it dead ends there), and turn left, then turn right onto International Drive, at the 7-11. The Publix will be on your right just before the next traffic light--you will probably see the Walgreens first.
For the closest Wal-Mart (brand new, by the way), take Sea Harbor to Central Florida Parkway, the road you would take to Sea World parking, but go the opposite direction, toward I-4. Bear to the right of the I-4 on-ramp, headed toward Turkey Lake Road. Turn right onto Turkey Lake Road (there's a light), Wal-Mart is a couple miles up on your left. Six or seven minutes, tops.