I don't know if I would leave them alone in the room, but (if you are sure they are responsible) there was a playstation in our room. I think it was going to cost about $7 per hour to play. I'm sure you can also rent movies, but I don't recall the price. Less than $10 as I recall. How many nights are we talking about, 2 or 3? If so 2 hours of Playstation and 1 movie would cost you less than $30 per night. Throw in $10 worth of snacks from the minibar and you've got two happy teens for under $40 per night. (You'll spend more than that on margaritas and hurricanes at CityWalk)
Or...You could take gameboy and rent loans of games. There is also a small arcade near the pool. Give them tons of money and turn them loose. Are board games an option? Cards? OR ...dare I say it, Books? (My eight year old would cringe) Maybe they'll be so tired from the parks and/or swimming that they'll just go to sleep. Wait..12 and 14..I guess not.
When are you going? I'd love to hear how this works out. I have young kids now, but I will be in your shoes soon enough.
HAVE A SUPER TIME!!!