I agree that the Museum of Belize is excellent -- it has many Maya artifacts, both on display and in stored collections. There are also Maya artifacts in visitor centers at Lamanai, Xunantunich, Caracol, Cahal Pech, Nim Li Punit and elsewhere. Also in some of the caves, such as ATM.
The archeology department vault in Belmopan has been closed to the public for many years -- mid to late 1990s? -- though at times in the past you could arrange for a private visit.