NoMachine client connection files (.nxs) are stored in the directory specified in the 'Player preferences' -> 'Settings' -> 'Folders' -> 'Connections and recordings' path, by default:

/Users/USERNAME/Documents/NoMachine on macOS
%USERPROFILE%\Documents\NoMachine on Windows
/home/USERNAME/Documents/NoMachine on Linux  

To migrate the connection files from one computer to another:

1) copy the .nxs files to the new computer and

2) copy also the .nx/config/player.cfg file from the user's home on the old computer to the new computer, because the list of favorites connections is stored there: 

/Users/USERNAME/.nx/config/player.cfg on macOS
%USERPROFILE%\.nx\config\player.cfg on Windows  (.nx on Windows is a hidden folder)
/home/USERNAME/.nx/config/player.cfg on Linux 

Troubleshooting

1) Note that the list of preferred connections is saved on the old computer  with paths of that computer. If paths on the new computer are different, they cannot work out of the box.

To fix paths, in player.cfg look for group:

<group name="Favorites" >

old paths to connection files are stored in "File" keys, for example:

<option key="File" value="/old_path_to/yourConnection.nxs" />

Replace each old path with the new path.

2) If you don't copy the player.cfg file, it will be still possible to use the old connection files on the new computer, but it will be necessary to load them manually. To do that, launch the NoMachine client via Programs menu/Application, click on 'Open' and load the connection file imported from the old computer.