The convenience store king of downtown Raleigh, Taz, has opened up Oak City Market House of Fresh in the Skyhouse tower. The shop is part deli, part grocer with a wide selection of produce, meats, and other essentials. What I like about this one is that the items are packed in there, as an urban store should be.
When you couple this up with DGX Raleigh nearby, you have some pretty convenient options along Blount Street.