Blue Moon Mexican Restaurant in Englewood, NJ is very good. 1st time I went I saw $10 or so for tacos & was appalled, but when I saw them literally hanging off the plate, I was ok with the price. Then when I tasted how good they were, it became a regular stop when visiting in-laws. Plus with the right bartender, 2 margaritas are the limit. WHEW!
I don't know north Jersey very well, but I'll give you some general advice...from my experience being married to a native Texan in NJ.
Barbecue. If you judge barbecue by Lockhart TX standards, you will likely be disappointed. I've never found decent Texas style barbecue in NJ. However, you might try Portugese barbecue in Newark.
Mexican. I have never found good Tex-Mex or northern Mexican food in NJ. However, there are lots of central Mexicans living in NJ. Their cooking is different and I'm sure there are many good places in north Jersey. The cities of Passiac and New Brunswick have large Mexican communities.
(I hope someone else will prove me wrong and post a recommendation for good texas style barbecue or tex-mex or fish tacos.)
Instead of trying to find Texan favorites, peruse this Mid-Altantic board and the Tri-State board. Discover what New Jersey does well. All sorts of Asian food, various Central American cuisines, Indian food, Portugese, Japanese, pizza, various Arab cuisines, and more.
Welcome to NJ!! Don't forget to visit a farmers market and enjoy some of NJ's excellent produce, notably tomatos, sweet corn, blueberries, peaches.