Some things are old. Some things are REALLY old.
I am a native westerner so “really” old to me may be new to an Easterner, or downright cutting edge to a European, but lets not get into that here. Lets just stay American for this one.
Colonial Williamsburg is great with all its reconstructed and reenacted sites. Jamestown is fine with all its folks dressed like one would in Colonial times. But I say they both get trumped by a big slice of history that needs no recreating. The College of William and Mary is alive and has been for over 300 years.
Let me put it this way; the guy who wrote our Declaration of Independence, which birthed our country, learned all those writing skills at this school. Thomas Jefferson’s Alma Matter was almost 100 years old by the time The U.S.A. was 1. The best thing about this school isn’t that it is old, but that it is still a school… a good one.
O.K. here is the challenge: name an institution in this country that has existed continually for over 317 years (quiet down Boston, we know, we know).
Enough of the old stuff, this place is a great spot to visit as well. The campus is surrounded by shops, cafes, and stores housed in colonial era buildings. The area is quite walkable and I say the Honeywell store is more than digestable.
Brohammas 
When I was 16, my aunt was teaching for a year at William & Mary. I went to visit her and became enchanted. I was determined to attend college there. Then I discovered how much it would cost. I then compared the in-state tuition of my local university that my mom received 50% off tuition for. I still dream about what my life would have been like going to the enchanting William & Mary.
It was kind of like boot camp. Tough.
Very pretty though and we are all proud of its history. W&M still has a Royal Charter.
I think Brafferton may be the oldest building on campus, I forget. It may have been the Indian school. I had a class or two in the Wren building and it was always fun to be stopped by tourists and asked if we were “real students”.