According to the Cryptobranchid Interest Group only a few zoos keep giant salamanders or Cryptobranchids and no zoo has successfully bred them within the United States. [View article from the Cryptobranchid Interest Group]. Below are a list of zoos that have them or are currently planning to place them on exhibit.
The National Zoo in Washington DC is constructing a major exhibit area which will be home to many Asian animals now living at the Zoo. The zoo's website states that both the Japanese Giant Salamander, Andrias japonicus, and the Chinese Giant Salamander, Andrias davidianus, are "exploring which salamander will do best on the Asian Trial". [View Giant Salamanders webpage at the National Zoo]
The Cincinnati Zoo currently has Chinese Giant Salamanders on exhibit with their Reptile house. [View Chinese Salamander webpage at the Cincinnati Zoo]
San Antonio Zoo has 4 A. japonicus on display.