The kids clubs start taking them at age 4. Last June we left the kids (then 4 & 8) at Simba's Cubhouse at the AKL while DH & I got to eat at Boma's (we were seated in the adult section - what a treat!

). We were staying at the AKL so that was very convenient. We only left them there for 2 hours and they were very disappointed when we came to pick them up!
In November DS was 9 and DD was almost 5 and we left them at The Neverland Club (we stayed at the Polynesian) for 3 hours this time. DH & I love the Kona Cafe and then we went over to the MK to try out Mickey's Philharmagic to see if the kids would like it. We also got to watch the fireworks and hold hands while walking down main Street. Sigh. So nice to have a place to leave the kids for a while so we could have some alone time.
The kids LOVED the Neverland Club and were not happy to see us even after 3 hours! DD is the arts & crafts queen and they had all kinds of things for kids to color, cut, glue, glitter, etc. They liked the buffet-type dinner since DS could get pizza (he's a very picky eater!). When we arrived to pick them up they were putting on a puppet show with a group of other kids. They had a blast!
I would not hesitate to leave your child at one of these places - especially if your child enjoys the company of other children and is ok with leaving you. They give you a beeper so they can contact you if anything goes wrong.
We are going back down in a couple of weeks and hope to get the kids back into the Neverland Club. Not sure how long we are going to leave them this time.

(It does get pricey tho with $10 per child per hour
Hope you have a great time!
Jill