Mariana, about 12 km away, is the closest and most rewarding day trip. The two towns were founded the same year and grew together in the gold rush, but Mariana is smaller, flatter, less touristed, and arguably has the most beautiful Brazilian baroque interior in the country at its cathedral. Get there by bus from Ouro Preto's main terminal (every half hour, 30 minutes) or by the Maria Fumaça tourist steam train (slower, more atmospheric, weekends only).
The other notable colonial towns of Minas Gerais — Tiradentes, São João del-Rei, Congonhas with its Aleijadinho prophets — are too far for a comfortable day trip but each makes a good onward stop for travellers building a baroque-towns itinerary.