Berlin: the Museum Island pass, and the Sunday flea market

The five museums on Museum Island (Pergamon's main hall is closed for renovation until the 2030s, but the Panorama and the Neues Museum's Nefertiti are open) share a day ticket that beats paying individually. On Sunday mornings, Mauerpark hosts the city's biggest flea market and, in the afternoon, open-air karaoke in the amphitheater. Tempelhof, the former airport, is now a park where Berliners cycle down the runways; it's free and vast.