I always bought into the notion that there were no supermarkets in the downtown zone. However, I noticed that there is a Kroger at 2nd and Breckenridge, across from the Spaulding quadrangle. It took me about 4 minutes to drive from Kroger to the Convention Center (2 red lights included). Heck, one could easily walk to it from Broadway in just a few minutes.
Now some may say that it isn't nice enough. If that is the case, Kroger could rehab it and put this notion to rest.