Radio Shack (and other stores) sell a converter to turn DVD player RCA and S-Video output into coax. About $30 or less.
Do be careful, I know *some* hotels monitor the cable signal to the TVs at all times to tell when they have been disconnected (i.e. to know when one is being stolen).
Obviously that's not the case with you!! But this might be one case where asking permission might be better than asking forgiveness?
Also, I have a friend with a portable DVD player (7" lcd screen) that has output jacks to play on a TV. More expensive than a cheapy DVD player, but maybe more useful? Just a thought.