If you have a laptop, all rooms have a dataport in the phone and you can plus in and dial up from there. I'd suggest getting the local access number from your ISP in advance. If you are staying at the Swan the high speed access from the room (with your laptop) is including in your room fees.
Without a laptop, some WDW hotels ahve business centers with high speed access, $40 per hour. BW, YC, Dolphin, CR, GF, CS would all have this service. Kinko's (I think it's on Kirkman Road--you can look for one on their web site) is probably a little cheaper, my bet is about $20/25 per hour, but I do'nt know for usre--that's just an educated guess.
Anne