San Luis Potosí makes a reasonable base for several very different excursions.
Real de Catorce (about 3 hours north) is an old silver-mining ghost town that was virtually abandoned for most of the 20th century and is now partially revived. You reach it through a mile-long cobbled tunnel in the mountains. The ghost-town atmosphere is genuine — ruined mansions, a roofless bullring, and a sacred peyote pilgrimage site used by the Huichol people — and the desert landscape around the town is extraordinary.
Xilitla and the Surrealist Garden (about 3.5 hours east into the Huasteca lowlands): the Scottish eccentric Sir Edward James spent thirty years from the 1960s building an open-air concrete garden of towers, arches, and fantastical structures in a cloud forest canyon. It is strange and wonderful and occupies the edge of a natural swimming hole. The drive east from San Luis Potosí descends dramatically from the arid highlands into humid jungle.
Santa María del Río (about 45 minutes south) is where the city's famous rebozos are made — the silk shawls woven so fine they can pass through a wedding ring. You can visit the weavers' workshops and buy directly. A pleasant half-day combined with a look at the hot springs at Ojo Caliente nearby.
For deeper exploration of the Huasteca region, the waterfalls at Tamul and Las Cascadas de Tamasopo require a longer drive east (3–4 hours) but are among the most spectacular in Mexico.