I haven't seen a thread on this subject, so let's do it! I'd like to leave Tex-Mex places out of the discussion unless they have a decent amount of authentic Mexican items on the menu, or something that's really unique and spectacular. And let's keep it east of I-95.
El Picante Mexican Grill
111 W Fire Tower Rd
Winterville, NC 28590
Probably the most gringo-friendly of the Greenville places. The owner and most staff speak English fluently, and they take plastic. They have several different types of tortas, tacos come in al pastor, tripe, tongue, chicken, and azada. They also have Nayarit style tacos(shrimp, fish, and breaded chicken), which have melted cheese and a special sauce whose flavor is hard to describe. They're very good though, and a unique item- I haven't seen this kind of taco anywhere else around here. The tacos al pastor are the best in town.
Supermercado El Rancho
2500 Charles Blvd
Greenville, NC 27858
This is a grocery store/carniceria that has an attached sit-down restaurant. The menu is a bit more extensive than El Picante, but I don't feel like the preparation is quite as good for most items. They have several really unique, somewhat baroque tortas- I've had a couple but the "española" sticks out in my mind, with its chorizo and egg. They also do really excellent fried quail. Birria and pozole are served on weekends. There's a good sized salsa/condiment bar.
El Rodeo Carniceria
102 Airport Rd
Greenville, NC 27834
El Rodeo is another carniceria, this time on the other side of town. I've only eaten here once and was pretty unimpressed. They had an impressive list of soups and stews which included birria and consomé de borrego, but I was told that they didn't have any soups or stews(despite them comprised about half of the menu). I ordered a couple of tacos instead, and both were pretty bad. The salsas had a bitter, acrid taste to them and were kinda gross. Avoid!
1200 N Greene St
Greenville, NC 27834
Right across the street from El Rodeo. I haven't been in probably two years since El Picante and El Rancho are so much more convenient, but I did have some pretty good tacos de chorizo there once upon a time. I'd like to go back and try there pollo azado- they make a big deal out of it being cooked over coals.
There are tons of places, but I'm really only familiar with Taqueria Guerrero, having eaten from their taco truck a few times in various places.
305 W 3rd St
Robersonville, NC 27871
This is a grocery store with a small attached restaurant. I just found out about it recently, so I haven't had the chance to sample it in any great depth. The major quirk here is that they don't have a menu- one of the employees will tell you what they're serving that day in so-so English. I had tacos al pastor when I went, and they were good. The salsas were above average, too.
Los Garcia's Store
6201 Mackeys Rd
This was a favorite of mine when I worked in Plymouth. Could use a status update, as I've heard that it has closed, but I haven't been down that way to verify. It's out in the country and has a country store atmosphere- many of the customers are non-Hispanic. My favorite was always the sopes and the green hot sauce.