You can find the answer to this in the flashback scene in Chapter 4.  This is where Jordan Baker is reminiscing about her younger days in Louisville. There, it says that all of the young officers from Camp Taylor would come to Louisville to hang out with Daisy.  So that is the name of the military base where Jay Gatsby went.

The official name of the place was Camp Zachary Taylor.  It was only built in 1917 as the US was trying to get a lot of soldiers trained for World War I.  At the time, it was 6 miles outside of Louisville.  It is no longer there, and a suburb of Louisville is called Camp Taylor.