A nice modern indoor swimming pool near the town centre.
Friedenssaal
Located in the old city hall, is famous for the signing of the historic Treaty of Münster, a document which, as a part of the Peace of Westphalia, ended the Thirty Years' War and established the Westphalian style of diplomacy between sovereign states.
The Prinzipalmarkt used to be the city's main market street. It was heavily bombed during the Second World War, but unlike elsewhere, where ruins gave way to faceless blocks of concrete, the houses were rebuilt, some following the original plans and some merely inspired by the old architecture. Try to spot to houses with identical gables (hint: there aren't any, but they're all pretty). Today it is home to many of the city's more exclusive (some might say posh) shopping establishments.
St.-Paulus-Dom
Münster is known for its vast number of churches that dot its entire cityscape, including Gothic St. Lambert's (Lambertikirche) and Baroque St. Clement's Church (Klemenskirche). The city's most impressive church, the St. Paul's Cathedral, is well worth a visit.
Schloss
It was finished in 1787 as one of the last major high-Baroque buildings in Germany (by that time Rococo and even Neoclassicist styles had already become in vogue), designed by Johann Conrad Schlaun, Münster's leading Baroque architect. Unfortunately, Prince-Bishop Maximilian Friedrich, who had commissioned the building, never got to move in there, having died three years earlier. His successor didn't bother much, and shortly thereafter Münster lost its status of prince-bishopric and the palace was used for other purposes. These days it is home to the university administration. During World War II, it was heavily damaged. The exterior was entirely rebuilt in the original style while the interior rather reflects the preferences of the 1950s. There's little to look at inside (although doors are open during university hours), but its façade is a curious and very characteristic combination of sandstone and red brick. During summer, lots of events are held on the square, somewhat marring the view more days than not.
You don't need to be a biologist to enjoy a lengthy stroll along the paths lined by some 8,000 different species. When the weather turns ghastly (it often does), you can seek refuge in ten greenhouses and pretend it's summer.
Late-Baroque country house, former residence of the poet Annette von Droste-Hülshoff, beautiful and well-maintained Baroque garden.