Westgate has a timeshare that is about 1.5 miles to the Merchant's Square area of Colonial Williamsburg. That's the closest one. You could try to walk from Patriot's Place to the Visitor's Center (about two miles), but you would have to cross major roads.
I'll have to ask another question though.
What are you planning on doing in Williamsburg?
Colonial Williamsburg could keep you busy for about three days, but there is also Jamestown, Yorktown, the historic Plantations, Busch Gardens, Water Country, etc. All of them are 10-20 minutes from Colonial Williamsburg and not walkable.
You need a car in Williamsburg to get from place to place.
I vote for staying at Manor Club and driving to where you want to go.
On the other hand, if you have time to stay for a few days and don't want a timeshare, I recommend staying in a Colonial House in Colonial Williamsburg. You will be in the middle of everything Colonial and the experience is really neat.