The Military History Museum sits by Piešťany airport, away from the spa promenades. Its collection focuses on military vehicles, aircraft, and equipment, so it is a good counterpoint to the softer image of the town.
It is worth the detour if you like Cold War hardware or are travelling with someone who needs a break from baths and parks. Check opening times before setting out, because museums on the edge of town can keep more limited hours than central sights.