The South Bohemian Museum (Jihočeské muzeum) occupies a substantial late 19th-century building near the main square. The permanent collections cover the natural history, prehistory and cultural history of South Bohemia, with some strong sections on the medieval history of the region including the Rosenberg family who dominated these lands before the Habsburg period.
The building itself is worth a look — the decorative stonework on the facade is among the most elaborate in the city. The museum is a good rainy-day option, and the scale is manageable: you can see most of it in two hours without feeling rushed.