The Palacio de Gobierno is worth entering for the murals by Desiderio Hernández Xochitiotzin. They cover the old Tlaxcalan dominions, the conflict with the Mexica, the Spanish alliance, and the long afterlife of conquest in local memory.
This is the most important stop in the city if you want Tlaxcala to feel like more than a pretty colonial square. The murals give the place its argument.