A couple of reference points of other GTK editors, both Xed and Gedit use home as their save-as directory when started from the menu, and the current working directory if started from the command line. I don't have a Geany installed as system so I can't try using the menu, but from the command line it follows the working directory (on Linux, IIRC Windows has some other working directory weirdness).
If save-as has been used this session Xed will use that directory for any subsequent save-as, it will not use the directory of any files just saved. Basically thats the same as the project-less proposal above.
Neither Xed or Gedit have anything like projects, so can't help there.