The drop off place is the Sandcastle Club - it's for 4-12 year olds. Kids nite out is a service that comes to your room - and will take any age. They seem pretty flexible and will even take your kids to a park or to dinner.
Here's some more info on Sandcastle Club -
http://www.mouseowners.com/info/showentry.php?e=31 I believe it's around $10/hour per kid with a 4 hour minimum - some other info on babysitting services at WDW is here:
http://www.intercot.com/infocentral/children/childcare.asp
We've actually used the Neverland Club for our kids and they absolutely loved it - they were 6 & 4 at the time. The children enter through Wendy's window and get sprinkled with Pixie Dust - the theming is very fun. Our kids didn't want to leave. A side note - they also gave us a pager, which was nice. Dinner was included, too.
We have a 20 month old, which is why we're trying Kids Nite Out this trip instead - he's too young for any of the other childcare.
Kim