The Bronx Zoo's grounds are land originally acquired by NYC as a park. Sate law would not allow the city to transfer the park to a private entity like WCS, so unless there was a special state legislative act at some point in history, the city still owns the land. The original grant in 1897 simply "allotted" the south part of the park "for the use of" the NYZS, which is not a transfer of title but basically made the NYZS a tenant. Something else may have happened since, but I can't find any historical reference to a transfer of title to the land. In fact, a search of current property records for 2300 Southern Blvd., the zoo's address, shows that that the owner is indeed NYC through the Dept. of Cultural Affairs.
Generally, in a situation like this, when the tenant builds a building, it presumptively becomes property of the land owner, so, unless the city and the WCS have a different arrangement (such as a 99 year land lease for the land underneath the buildings, with the WCS owning the buildings, which is another way such situations are sometimes handled), the city also owns the buildings.