The multistory Progreso Market has more than two dozen shops featuring arts and crafts from all over Mexico as well as a grocery section and a pharmacy. It is enclosed by a wall and offers a bit of refinement not found out on the main street. The shops did not seem to be as crowded here as on the main strip. Perhaps this was because it was at the far end of town from the bridge, and many tourists just don't seem to make it this far, although it is only a few blocks walk.
The main drag just across the bridge is the "zona centro" of this little town, just like in other border towns. It's a great place to shop, eat, and drink. Plenty of bars and restaurants up and down the main calle (street). One of the safest border towns I know of. I go there at least once a year and have never seen any cops, only private security gaurds.
Park at Arturo's restaurant. Grease the parking lot gaurd with a $5 and you'll be fine.