Long-distance trains use Kassel-Wilhelmshöhe, not the old central station. The ICE network puts the city within easy reach: Frankfurt (1h30m), Hamburg (2h30m), Munich (3h30m), Berlin (3h). Buy tickets in advance for the best fares.
The nearest international airports are Frankfurt and Hannover, both around 2.5 hours by train. The small Kassel-Calden airport handles a few low-cost flights but is rarely useful. By car, Kassel sits at the intersection of the A7 (north-south) and the A44 (east-west), placing it about three hours from most major German cities and an easy stop on a Hamburg-Munich or Brussels-Berlin road trip.