Northern Europe
In Berlin, the Museumsinsel day pass lets you move between five buildings under cover. In London, the free national collections mean a wet afternoon costs nothing at all. In Copenhagen, the winter garden at the Glyptotek is the warmest room in Scandinavia.
The Netherlands and Scotland
Amsterdam puts three great museums on one square, so the walk between them is ninety seconds. Edinburgh is built for rain: the national galleries are free and the Old Town has more indoor space per street than anywhere in Britain.
Southern Europe
Paris has the covered passages and the Orangerie, which needs an hour. Venice floods rather than rains, which is a different problem, and the answer is the Accademia. Milan has the Galleria and Brera five minutes apart.
The Americas and Asia
New York keeps the Met open late twice a week. Mexico City rains hard for two hours in the afternoon and then stops, which is exactly the length of the anthropology museum upper floor. Tokyo has the Roppongi museums open until ten, and Seoul has a free national museum the size of an airport.
The universal answer
A gallery district. They are free, indoors, clustered within a few blocks and nobody minds a wet coat.
