You can take a dip in the Olympic Pool Complex or ride up the 290m Olympiaturm, the tower at the Olympic Park where the games took place in 1972. There is an array of museums to amuse, from the Deutsches Museum, a science and technology delight, and the Bayrisches Nationalmuseum about the lives of past Bavarians, to the BMW Welt, which is yes, you have guessed it, all to do with the famous car manufacturers.
Palaces feature highly on the must-see list, starting with the Residenz, where Bavarian rulers lived from 1385 to 1918. The museum connected to the palace is a plethora of information and treasures from that time. Schloss Nymphenburg was the royal summer residence and is worth a visit, even if it is only for a meander round the glorious gardens.