Bar Fun Fun in the Ciudad Vieja is one of Montevideo's oldest bars, with a long association with tango — both Uruguayan and Argentine artists have performed here, and the walls are covered in photographs of musicians who passed through. It has the dark wood panelling, the mirrored shelves, and the general air of a place that has seen better days and is comfortable with that fact.
Tango performances happen here on certain nights; check the schedule. Even without a live performance, it's a good place for a late-night drink in the old city — beer, whisky, and the usual Uruguayan spirits. The clientele mixes locals with tourists who've been pointed here by their hotels.