Once Tapachula [1]’s city hall, the lovely Museo Cultural y Turístico de Soconusco (Parque Hidalgo, 8a Av. Nte. near 1a Calle Pte., 9 a.m.– 6 p.m. Tues.–Sun.) functions more as a cultural center than a museum. Stop by for a schedule of events; in addition to offering art workshops, it often has art exhibitions and events.
The Casa de la Cultura de Guatemala en Tapachula (4a Av. Sur 25, tel. 962/625-0356, apuertaabierta [at] hotmail [dot] com, 2:30–9:30 p.m. Wed.–Thurs., 9 a.m.–11 p.m. Fri.–Sat.) often has live music events and special performances, most highlighting Guatemalan culture (of course). If you’ll be in town awhile, consider signing up for one of its popular cooking, music, or writing classes.
Links:
[1] http://www.moon.com/destinations/chiapas/the-pacific-coast/tapachula