People go to Nogales daily from Arizona. Many, many have dental work done there. If you stay just across the border you'll be perfectly safe and that's where the shops and restaurants are. There's no need to wander farther in - that's the residential area. That's the same as any border town. You can easily park on the Arizona side and walk across the border. You'll be walking with other American tourists. Talk to them as you walk to get hints on where to eat, etc. Chances are they've been there often.
The above-mentioned 'war zone' is not happening at the border. Why would the druggies, etc. be right there? They don't like to mingle with the Border Patrol! :)