I rarely travel with one lense for my Nikon unless I am just planning on taking specific types of photographs or plan on setting my camera features allowing me to obtain quality photo after I crop the original photograph(s). I carried my wide angle-standard zoom lense with me everyday at Disney along with my 50mm f1.4 to shoot in indoor-existing light conditions.
If you want to take pictures of the castle, landscape or wide scene while also taking photographs of family or firends then consider a wide angle-standard zoom ...typically 17-70mm (25.5-105mm in 35mm camera lense terms) which is economical too and provide good wide angle capabilities and allows you to take good portrait shots. I think at Disney this will cover 70-90% of your photo needs.
Shooting with a 70 or 80-200 zoom limits your ability to shoot wide angle scene type shots or shooting pictures where you are confined and you want to get a lot of things included in your composition. Lot of places at Disney are confined due to building structures and people, but this type of lense is ideal for portrait and telephoto shots.
If you just want to take one lense then take a wide angle-standard lense zoom, since if you set your camera properly you can always crop your photo to obtain a closer image of something farther away. Also, this lense will be lighter and easier to transport around than a telephoto lense which others have mentioned, especially if it is F2.8 or faster. The lense elements in the faster telephoto lenses are rather heavy and carry the burden and stress related to protecting these expensive assets. Cheaper versions are available too, which are light weight since they are barrel zoom lenses (70-300). I often left my f2.8 zoom lense in the resort safe, since I was getting the shots I needed with my other lenses, but I still used it on a less frequent basis.
Just remember. Each Disney resort have room safes so you can always leave a lense in your rooms safe. It appears each resort provides a different size safe, but the fron desk also have safes too if you would happen to find your room safe to narrow or shallow.