I stayed there in January a few years ago. Like someone else said, the World Center isn't close to anything. I would definitely rent a car. (I was there for a conference, so I only got to spend one day in WDW. It was OK for that, but I can't imagine spending every day on this shuttle system.) Basically, the shuttle system there is lousy. It's run by Mears and is fairly expensive. (Like $8-$10 per person, per day.) They only run two or three "To the parks" shuttles in the morning and only two or three "From the parks" shuttles in the evening. You can only go "To" in the morning and "From" in the evening. So, if you want to go back to the hotel in the middle of the day, you're basically screwed. And if you miss the shuttle, it's at least an hour until the next one.
There is a Courtyard by Mariott near Downtown Disney that's also nice. It's smaller than the World Center and doesn't have all of the perks, but it's WAY more convenient to WDW and even has the Disney Shuttle service included. It's within walking distance to DTD.