Things to look for, in no particular order:

Wicked Weed: Sours and farmhouse ales in bottles. Serenity, Oblivion, Genesis, and Black Angel are fantastic. They don't bottle continuously, so it'll vary from store to store what they have. I think Oblivion (sour red) and Amorous (sour IPA) hit the shelves again recently, so you might have a decent shot at finding those around.

They don't bottle their other styles yet, but Wicked Weed has an awesome DIPA called Freak of Nature and makes lots of other wacky stuff. Wicked Weed is particular about where they send their kegs, so you probably won't find their stuff at every bar.

Olde Hickory: Solid brewery that's responsible for some of the "whale-iest" beers in the state. Event Horizon is their BBA imp stout. Lindley Park is another BBA imp stout, but with raspberries. They recently released Omega Point, a delicious BBA barleywine. I don't know if Omega Point is going to see distribution, so you might have to trade if you want it.

NoDa: Hop, Drop, 'N Roll won a gold for IPA at the World Beer Cup last year and has since blown up in popularity. It is available in 4pks, but the brewery self distributes and quantities run out fast. If NoDa hasn't made a delivery in a while, you might have to call ahead to find it in stock. Coco Loco is a solid coconut porter and Jam Session is a really enjoyable session pale.

Foothills: Sexual Chocolate is probably their most well-known beer outside of the state, a russian imperial stout. Bottles have probably been off the shelf at most stores for a while, but kegs are still popping up around for bars throwing special events. There is also a BBA version, but you'll need to trade for that. Their Jade IPA (available in bombers) is one of my favorite IPAs in the state and (IMO) is better than NoDa's HDR when fresh. Seeing Double (their yearlong DIPA) is also solid and is sold in bombers.

Triple C: BBA Chocolate Covered Pretzel Stout is their new release, and I dig the hell out of it. Their Up All Night Breakfast Porter (and corresponding BBA version) is also good.

Gizmo: Their bottles just recently saw distribution in my side of the state, and they have a couple good options right now. I haven't tried them all, but their Aztec Gold (imperial stout, with extra chocolate and vanilla) and their Black Stiletto Coffee Stout are solid.

Green Man: Their flagship line are all decent english style ales, but their sours are top-knotch. Snozzberry, their next sour release, is supposed to come out soon. It'll probably sell out at the release event, but be on the lookout if it sees limited distribution.

Duck-Rabbit: The Duck-Rabbit Milk Stout is the standard milk stout for the region. Their Barleywine is out now and is also fantastic.

Mother Earth: Silent Night is a BBA imp stout you might still be able to find around. It is (IMO) one of the most under-rated beers in the state.

There are tons of more great beers from NC breweries out there, too. Just ask your bartender/bottle shop worker and they'll point you in the right direction.

For non-NC breweries, NC recently(ish) got distribution from DuClaw, Prairie, Cambridge Brewing, Troegs, and (in some places) Westbrook.