I've got both 1.22 and 1.23 on my USB thumb drive, along with the Granddog USB install folder.
Works practically anywhere unless you're on a really, really restricted computer.
You basically need to be able to install the dongle detector to play the game, and if you want to copy track records (not discs - discs are stored on the dongle) you need access to the My Documents subfolder where DJMAX stores all those. Copying them back and forth works perfectly.
You can export the TR registry from your original PC and merge it on the new location just so that the patcher/launcher shows the correct version, although this isn't absolutely necessary, I guess, since it's highly unlikely for patches to come out anymore.

TR.exe bypasses the launcher/patcher completely.
edit: I've had a bazillion people ask me what game it is @ internet cafes. :V In some cases people a few computers over started youtubing for DJMAX.