Go out onto Kirkman Rd from the HRH (that would be making a right exiting the HRH & then the first left you can make at the light.. that next light is Kirkman. Make a left onto Kirkman & stay in the left hand lane. Go up to Conroy Rd.. think it is the second traffic light. Make a left onto Conroy & get into the right hand lane, you will see Publix on the right hand side a few minutes down the road. If you make a right onto Kirkman & head over the I-4 over pass, you will see a very large Super Target accross from the Mall of the Milennia.. Target on the left, mall at the light. That trip is further then the Publix trip...
forgot to mention that the Super Target has a grocery store in it.. there are not super Walmarts that I can think of that would be closer than Publix or Super Target...