For the basket, if you think he'd use it in the parks, I'd use a backpack instead of a foldable cooler. Unless you plan to pack your lunch - then the cooler might be useful. I just don't see it as useful otherwise. If neither a backpack or cooler would be used, then I'd just cover a cardboard box in pretty dollar store Spring wrapping paper and use that as the basket, filled with a bit of Easter grass. But I'm cheap

and hate spending money on things that won't be extensively used (I even save our Easter grass and reuse it from year to year LOL)
DD15's Easter basket this year is a new suitcase for our summer vacation - that is an idea too, if he needs one. I'll leave it out opened, with all the other stuff the "Easter Bunny" is bringing prettily arranged inside.
For the contents, how about:
- Bug wipes. While Disney is great with insect control, it can still get a bit Mosquito-y during the nighttime shows if there isn't a breeze. And the wipes are easier to carry - just take one or two with you instead of a whole a bottle.
- Any camera accessories he might need, if he uses one (new SD card, Disney-themed neck strap, etc.)
- Some favorite snacks, in single-serve packs. I love Disney snacks, and indulge in them regularly, but sometimes you want just a little something while you are in line for a ride, back in the hotel room, etc. If he's a gum chewer, include some of this because its hard to find. (If I remember right, they don't sell it in the parks but might at the resorts?)
- Moleskin. I won't travel without it. With all the walking at Disney, even the best broken in shoes can cause problems.
- Rain poncho
- Filtered water bottle. I prefer using one of these to spending a fortune on bottled water. The filter works great to remove any odd tastes. And there are plenty of water fountains where you can fill them up. (
Disneyland even has some chilled water fountains, you just need to know where they are - water comes out wonderfully cold even on the hottest days - not sure if WDW has the same or not, we've just always gone for the nearest one there)
- Hidden Mickey book.I personally never really got into the whole hidden-Mickey thing other than at the most superficial level, but if you think he'd might like it, go for it
- Quarters and pennies for the pressed penny machines, if you think he'd like that. DD really like doing them, so I went so far as to buy old, 100% copper pennies off of eBay.
- Sunglasses if he needs them.
- Hat to keep the sun off
- Packing cubes, if he's into organization
- Travel size toiletries (toothpaste, etc)
- Disney-themed Tshirt
- New pair of swim trunks