Østerbro Svømmehal is a public swimming hall in a restored 1929 building, with a broad glass roof and a faintly Roman-bath feel. It has ordinary pools and spa facilities, but the period setting makes it more interesting than a routine sports centre.
It is a good rainy-day stop in Østerbro, especially if you like historic public buildings that are still used for their original purpose. Bring swimwear rather than expecting a museum visit.