The Rotes Rathaus (Red Town Hall) is the seat of Berlin's governing mayor and a red-brick neo-Renaissance pile completed in 1869. Outside, note the terracotta frieze that illustrates Berlin milestones until 1871. Except during special events, much of the town hall is open to the public – pick up a brochure with a self-guided tour in the foyer and also check out the free special exhibits.
The moniker 'red', by the way, was inspired by the red brick facade and not (necessarily) the political leanings of its occupants.