You can definitely have stuff sent to the hotel. We've done it a few times. Get the actual address from either the back of your hotel reservation sheet, or AllEars has the addresses in their accomodations seciton at the bottom of each hotel's FAQ.
http://www.allearsnet.com/acc/faq_hot.htm
Two things that you need to make sure the sender includes on the package: The package should be addressed to the person whose name is on the reservation, and your check-in date should be noted somewhere near the address.
As for mailing a package out, that's a bit more complicated. The resorts usually only handle stamped letters and postcards. If there's a way that it can be pre-postaged or pre-paid for UPS or FedEx, you could perhaps ask the hotel front desk to put it in with their own outgoing packages. That's something you might want to call the hotel directly and ask.
There's also offices at most (if not all) of the hotels with conference centers (Contemp, GF, Yacht & Beach, Boardwalk and Coronado) where you can pay for use of office equipment like computers, copiers, fax machine, etc.
Apart from that, you'd have to venture off-site to find a post office if you have a car. I know there's one in downtown Celebration.
-Rob
