In room is wired for concierge. There's no free wi-fi you can use with your phone. What I'd suggest doing is using your phone's ability to connect to the Verizon network, you generally pay per mb through Verizon. Just add it to your plan before your trip and if's not something you want to keep on it, then take it off the next month. Because a packaged price like that is cheaper paying per mb.
And if you are staying in a Disney resort, the last time I was there, it was 10$ or so to use the cable to connect to the net through your room per day, and there's a per hour charge too if you're going to be on less than an hour.
I have AT&T and pay 5$ once a month for 1mb of net access. Each page I open is just a few kb because I only use it for yahoo, and always open from last address, so I spend less time opening pages to get where I want. My phone doesn't have wi-fi abilities, so I can only use the net through AT&T network.