Kanchanaburi

Both work well. As a day trip by train (2 hours each way) you can easily cover the bridge, the war cemetery and the JEATH museum in one day. But staying overnight adds a lot: the floating bungalows on the Kwai Noi, the train ride to Nam Tok and a day trip to Erawan or Hellfire Pass are each worth half a day. Two nights is ideal.

By train from Thonburi station (not Hua Lamphong), 2.5 hours, very cheap and atmospheric. By bus from the Southern Bus Terminal (2 hours, 100 THB). By minivan from Khao San Road (private arrangement, 2 hours). The train is the most scenic route but departs early (7:45 and 13:45).

The bridge is an icon, but the museums provide the context. My recommendation: start at the war cemetery (emotionally heavy, small and austere), then visit the Thailand-Burma Railway Museum (extensive, well done), then walk to the bridge. This way you'll understand the bridge differently than if you visit it on its own.

The park is open year-round, but the waterfalls look their best and are easiest to walk in the dry season (November, April). In the rainy season (May, October) the water can turn very brown from mud and the higher levels are sometimes closed. The park gets very busy on Sundays, so go on a weekday.

The Erawan Waterfalls are wonderful for children: swimming in the pools, fish nibbling at your feet. The floating bungalows on the river are an adventure for children over 6. The historical museums are recommended for children over 10, as the subject matter is heavy. An elephant sanctuary is also an option (avoid riding).