The most rewarding day trip is to Silvia, a small market town 60 km northeast of Popayán where the Guambiano (Misak) indigenous community gathers on Tuesdays. The market is one of the most visually striking in Colombia — the Guambiano still wear their traditional blue-and-fuchsia ponchos and bowler hats — and is a working market for the community, not a tourist set-piece.
Further south, Coconuco has hot springs in a high-altitude landscape that is genuinely Andean, and the slopes of the Puracé volcano offer good day hikes for fit walkers. Reach all three by colectivo from Popayán's bus terminal.
The road east into Tierradentro and the famous underground tombs is technically a day trip but is better tackled with at least one overnight, given how long it takes to get in and out of the valleys.