All manner of arts and crafts are sold at the artisans markets held in Plazuelita Las Tres Palmitas and elsewhere around Plaza Mayor [1].
For cigars and rum, head to Casa del Habano (Maceo, esq. Zerquera, tel. 041/99-6256, daily 9 a.m.–7 p.m.) or Casa del Habano y Ron (Martí, esq. Lino Pérez).
The Casa de la Música (Juan Manuel Márquez, e/ Bolívar y Menéndez, tel. 041/99-3414) has a wide selection of CDs. Musical instruments can be bought at the Taller de Instrumentales Musicales (Menéndez #127-A, e/ Ernesto Valdés y Colón, tel. 041/99-3617), where bongos, timbales, etc. are made.
Much of the ceramic work sold locally is made at El Alfarero Casa Chichí (Andres Berro Macias #51, e/ Pepito Tey y Abel Santamaría, tel. 041/99-3146, daily 8 a.m.–8 p.m.), where the Santander family carries on a tradition of pottery-making.
Links:
[1] http://www.moon.com/destinations/cuba/sancti-spiritus-province/trinidad/sights/plaza-mayor