By the time the Tennessee 5th Infantry arrived in Mexico in January or February 1848, most of the major battles had ended. They were charged with guarding the Puente Nacional (or National Bridge) on the road from Veracruz to Mexico City. The bridge still exists today (see the Wikipedia entry). It was built in 1806 and originally called the Puente del Rey.
There are quite a few accounts from soldiers who fought at the bridge and traveled through the area. I'm going to link to some of these accounts here in order to keep track of them for reading later.
Service Afloat and Ashore by Lt. Raphael Semmes is worth a full read.