There is a regular bus to and from Durazno from Montevideo with departures all day long. The trip takes about two and a half hours each way.
You can just walk around, it's a small city. There are taxis waiting at the bus terminal though.
Pan y Vino is a popular place, located in the same building as the bus terminal. There are also various restaurants in Gral. Manuel Oribe and around the various plazas.
Two bars in Gral. Manuel Oribe, near the bus terminal. Gets crowded around 1-2 a.m. Fridays and Saturdays.
Hotel Central offers singles for 33$ and doubles for 63$.