One of the things NB is famous for is Fiddleheads. (It's in the title of this thread after all), but that is a seasonal food that restaurants don't really serve. They are just coming into season though, so they might be available if you look/ask around a bit. (Especially in the Freddy/Saint John River Valley area). I don't care for them myself, but it is well known.
For Lunch options in Frederiction, Moco's downtown is an excellent choice. The other downtown restaurants like Snooty Fox, Lunar Rogue Pub, Dolan's, MidSea Eaterie and Issaac's Way are all good choices (but I'm not sure how many are open for lunch; they may only be open for weekday lunches and dinners).
Outside of Downtown, there are other options like J's Asian (which is on the Northside AND Downtown), Woolastok Wharf, Pine Tre Pub, Red Lantern Inn, Mama's Pub (all on the Northside), and Ringos. (on the top of Smythe street) and probably more places that I can't think of at the moment.
I don't think there are really any New Brunswick only chains, because the Maritimes tend to be too interlinked; any chain quickly goes to all 3 provinces. As for Maritime only chains, there are a few, mostly fast food places. Greco, Pizza Delight, Dixie Lee Fried Chicken, and Deluxe Fish and Chips are the four 'big' ones in the region and are all decent enough for Fast Food options. Taco Boyz has 2 locations in Freddy and some in PEI and is a great option too. There are other restaurants (mostly pizza places actually) that are regional; like Tony's (2 locations in Freddy) and more.