Consider a trip to the local Wal-mart - there's one on I-192 in Kissimmee - and buy the cheapest VCR you can find, with a couple of screw-on (unless you want to risk higher signal degradation with cheap push-on) cables. Disconnect the cable from the back of the TV, routing it to the tuner input on the VCR and connect the output from the VCR back to the TV. Perform VCR tuner setup operation and you'll be able to record directly to VHS.
I've done this a couple of times - leaving a $40 VCR behind once - and have fed the composite out and audio signals into my miniDV camcorder for even better results.
The set-top boxes at the Tokyo Disneyland Resort hotels made it even easier - unplug the composite and audio cables from the back of the TV and plug into the inputs on the camcorder... I had to monitor via the camcorder LCD and speaker but it worked great.
Things aren't always as bolted down as they originally appear. A pair of pliers and a multi-bit screwdriver can usually make the cable connection on the back of the TV available... I rarely travel without them in my checked luggage.
A more "permanent" solution which doesn't involve throw-away hardware might be to find a USB TV tuner - make sure it tunes "cable" as well as over-the-air analog and digital (HDTV) channels. Set it up on your laptop and route the cable from the wall to the USB tuner. You'd then use whatever PVR application is supported by your hardware to record the channels. After proper channel setup you might find - depending on the resort - an "extra" channel which isn't programmed into your room TV: the "keep kids occupied in the lobby" channel which shows cartoons and Disney movies 24x7. It's good to explore.
