1) Goethe, Beethoven and Franz Joseph the First were all regular guests to the mineral baths and spa treatments here - and you'll be able to follow in their footsteps without the Spring/Summer tourists.
2) There's a big aquatic center called the Aquaforum where you can easily while away 4 warm, relaxing hours for about 200kc (120kc more for the sauna, too).
3) Someone yarn-bombed lampposts and flower planters in the center, and it looks like they're wearing sweaters.
4) You can "take the waters," i.e. drink the highly carbonated mineral spring water from fountains scattered around town. The taste is vile but it's supposed to be very healthy; you can get rid of that Winter cold.
5) The chilly evening temperatures will cause you to seek refuge somewhere warm and you may stumble upon a gem like the Country Saloon Bažina, an "American" country bar. The night we went, a band played Kenny Rogers and Alan Jackson in Czech! (They need to ditch the flag on the left, though.)
6) There are numerous parks, and many hotels offer Nordic walking tours through them with all the retirees (who are basically the only other people in the town besides you).
7) The grand 19th century architecture is striking - no matter what time of year you come.
8) You might quietly spot a celebrity in a cafe. We saw Czech comedian/actor Lukáš Pavlasek while we were eating this afternoon snack.
9) There are a number of peaceful spots to pop into, such as the Russian Orthodox Church of Saint Olga.
10) It's just a lovely cure for the long Winter doldrums.