Kayseri's National Struggle Museum occupies a central historic building and focuses on the years around the Turkish War of Independence. The exhibits are most useful if you already have a little context for the period: local names, documents, photographs, and schoolroom-like displays explain how national history was experienced in a conservative Anatolian city.
It is a good secondary stop after Kayseri Castle and the older Seljuk monuments. The museum gives the modern republic a place in the city itinerary, and its central location makes it easy to fold into a walk through the old commercial core rather than treating it as a separate excursion.