Juarez has a great selection of restaurants that specialize in authentic Mexican cuisine. The cuisine in Juarez is not very different from the food that is eaten on the the other side of the Rio Grande in El Paso. A great dish to try for those not experienced in Mexican cuisine would be Steak Ranchero.
Juarez also offers a very international selection including everything from great seafood at Los Arcos, incredible chinese at Shangri-La, Brazilian at Fogueira, and the list continues. Try Maria Chuchena for a nice semi-expensive eclectic meal, afterwards walk out to La Cantera where you can find restaurant/bars to have a few drinks with the locals. Unfortunately, the recent crime wave has shut down many of these establishments.
There are also many small stores and carts that make tacos using fresh tortillas, vegetables, and your choice of several meats such as beef, chicken, pork, and chorizo (a spicy Mexican sausage). As long as you can see the meat being cooked you should feel fine eating this food, although it may be outside of some inexperienced travellers comfort levels. Tacos are served "by the order" and you should not expect to pay more than 30 pesos or $3 for an order of 4.
As Juarez is a major city there are some very nice steakhouses where you will be pampered by an exceptional waitstaff in a luxurious setting. However, expect to pay about half of what you would stateside. A delicious steak dinner with all the fixings can be had for around 100 pesos, $10.