I would have posted this earlier but when I tried, the software would not let me.
I worked in Cuidad Juarez quite frequently ten years ago. Basically, I stayed in El Paso and crossed the border each morning to head to work.
The best place in the area is Cattleman's Steakhouse at Indian Wells Ranch which is about 35 miles east of El Paso.
Indian Cliffs Ranch
Fabens, TX
915-544-3200
Take I-10 east to exit 49, turn left and travel about five miles into the desert and you're there! Open daily for dinner and lunch and dinner on Sundays.
Besides great steaks, they also allow you to wander through the ranch and they have a number of great animal exhibits. The last time I was there, I saw a pack of coyotes as well as some other animals.
Another good place is the State Line BBQ which is part of the County Line BBQ chain. (referred to by the previous poster.)
The State Line