Every day on the train I hear them announce what side of the train the platform will be on. Every time it's something like "platform will be on the right-hand side in the direction of travel". Now, there are a couple of terms already for the left- and right-hand sides in the direction of travel: port and starboard. People might not be quite familiar enough with them to get it right away, but I think they would catch on soon enough. What do you think?
Mokalus of Borg
PS - If I were making the announcements, I might do it just for fun.
PPS - And then I'd probably "ARR!" like a pirate.