Technically the closest grocery store would be Goodings. That is about a mile down from DTD. But, Goodings happens to be about 5x more expensive than the others. If you get to Hotel Plaza Blvd. take that all the way out to the major intersection. Not sure what the name is. You will have a 4-way stop. You can go across the street to Goodings and a strip mall. Our choice is to make a left at that light and go down about a mile. On the right hand side is WinnDixie. Their prices are very reasonable. Very comparible to Publix.
P.S. If anyone can jump in and label that 4-way street, I would appreciate it! I want to say it is 535, but I am not sure!!