Hey there Daria,
I might be worthwhile for you to make a weekly trip to Carrboro/Chapel Hill or Durham. Wednesday and Sat morning are Farmer's Market days, Sat is in Durham. All local foods, locally grown. The one in Raleigh is a little more uncertain to me, but does have some good stuff.
For fish, I'd check out Tom Robinson's Seafood in Carrboro - it's all local catches from the coast. They bring the catches in on Thursday.
You could also check Cliff's meat market in Carrboro, it's a locally owned butcher and they have some interesting cuts like 'elk' sometimes.
Personally I do most of my shopping at the Farmer's Market. It's cheaper, fresher, and more personal. there are a bunch of CSA options in the Triangle so you may want to check that out as well. If you are working in the park, there is that bbq place on 55 - though I'm not sure where they source the meat. There is also the Korean place and Neomonde is awesome too, Oh .. the Cuban place can be ok - lots of primal options there.
Oh here is a link to my yelp list - though not everything is on it.
Primal Blueprint Friendly - Chapel Hill