personally, i would go for the lilo/stitch breakfast at the polynesian... i cannot wait to take my son there (could be 'cause he resembles stitch! LOL!)... although since you are staying there, it may be part of your plan already, so substitute chef mickey's or 1900 park fair...
maybe followed by a ride on the monorail (asking to sit up front and get a pilot's license, of course)...
do you like boats? rent a water mouse/sprite boat from one of the resort marinas, i know they were quite the hit when we did it (ds was also 4yo at the time)
maybe head downtown to the new pirate room for some dress-up fun...
and play in the
legoland playground and have ice cream at ghiradelli...
or head over to the campground and go on a hayride and see the horses/petting zoo w/buffet at trail's end...
perhaps a water park would be a great fun adventure for the two of you, if you're not going another day... or visit the AKL to see the animals...
maybe mini-golf at winter/summerland...
as you can see from my suggestions, my opinion is if you will be visiting the parks on your other days, i would do some special out of the park stuff for your one-on-one day... otherwise when you go to do the park stuff w/dad, it will be "old hat" to ds if he had just done it the day before (or vice versa)