I nearly forgot--Hatch, home of the "world-famous" Hatch chile peppers is on the road from Socorro to Las Cruces. So, if you are a fan of green chile, be sure and stop there. They may not be "just-picked" that time of year, but you will be able to get some roasted chiles to take with you.
Just south of Las Cruces is one of the largest pecan-growing areas in the nation. So, a visit there is also a delicious way to spend an afternoon.
And, finally, southern NM has become quite a wine grape-growing area too. You may not get Pacific NW-quality wines there, but it is still fun to visit some of the tasting rooms in Las Cruces.