Tom, we've been to Nogales a number of times and always park on the US side and walk across. There are a parking lots (for cars or small vans) within a block of or two of the crossing point. They usually charge about $5 to park.
Just got back from Nogales. We parked for $3, easy walk into town and easy re-entry. (We had our passports with us and they appeared to give us an edge in terms of speed of processing at the border).
Once we were south of the border, it felt a bit like Tijuana - larger than Algadones and not as easy to find the places we needed. Lots of pharmacies around, but prices varied significantly. Eyeglass places were tougher to find and, even when I tipped a local to find me one, they had a very poor selection. I put it down to our lack of familiarity with this town.
But, we did save quite a bit of money, just as we have when we've visited Algadones.