First off, how old is your child? If he/she isn't 4 years old, Florida law says he/she cannot stay at the resort run kid's clubs ( daycare, if you will). You would have to get an in room babysitter, and there are 2 very reputable services that serve the WDW resorts. The most popular is the Fairy Godmothers.
As for the resort childcare. It is very reputable, licensed by the state of Florida. You can request to see the licensure if it makes you feel any better. Our favorite is the Neverland Club at the Polynesian. (It is open during the day from 12 to 4 for kids and parents to go and play, which may be a great way to get a feel for it before you decide if this is what you want to do.) Dinner is provided with this service, and the cost is $10 per hour (it just went up in September). They have a buffet style meal. There is a big movie theatre screen playing Disney animated films, there are centers with arts and crafts, computers, video games, and "let's pretend" areas with dolls, "play house" type toys. Our DD always comes home with all kinds of "creations" she has made at the arts and crafts stations. The workers are very attentive, and help the kids with their projects, etc. You are given a beeper so that if there is any problem, they can reach you, and also you are given the phone number, so you can call at anytime.
We felt very comfortable letting our child stay here, and in fact it is one of her "must do" activities on our WDW vacations! I can't speak highly enough about the facility or the staff!
Other activities in which our DD has participated include the Wonderland Tea Party, which lasts an hour and is at 1900 Park Faire on select afternoons. The kids decorate and eat cupcakes and drink "tea" (apple juice), Alice reads to them, and they make arts and crafts projects. I believe they start letting children of 3 participate in this, as long as they are toilet trained. The other activity was the Pirate Cruise, which was also wonderful! This an a 2 hour activity, and the kids actually go out on the boat and stop at the beaches of the resorts to hunt buried treasure. There are 4 chaparones on this, and 2 are certified lifeguards. The kids are fitted with regulation lifevests, which they are required to wear at all times. My DD thoroughly enjoyed this, as well! The castmember in charge of the 2 above mentioned activities is Drew, and he is wonderful with the kids.. and has been doing this for years!