I prefer to leave downtown for meals. Mostly because I've known people who worked downtown and that just spoils you on the management.
Not so far away is Fiery Ron's Home Team BBQ.
http://hometeambbq.com/ Fave grits. Good pork. I've never eaten a "wrap" in my life (hate 'em anyway) so I can't comment on their wraps. All other food is good.
You can always hit up one of the Bessinger family's restaurants for golden sauce and pork. Bessinger's http://bessingersbbq.com/home/default.html or Melvin's http://www.melvinsbbq.com/. If you're ever way north, you can hit Piggy Park in Columbia or Duke's in Orangeburg.
No one can ever say I don't love me some golden piggy bbq and grits.