Although it doesn't get nearly as much attention as the National Museum, the gallery's permanent collection (modern and traditional Thai art) is worth taking the time to see; there are also frequent temporary shows from around the country and abroad. To get to the gallery, walk down Na Phra That Road, past the National Theater and toward the river. Go under the bridge, then turn right and walk about 100 yards; it's on your left. The building used to house the royal mint.
Chao Fa Rd., Bangkok, 10200, Thailand