In my neck of the woods (Boston area) Williams has the same prestige as Stanford, and its reputation academically as the top “little Ivy” is top notch. I would consider the fact that the focus is on undergrads in a small, high end liberal arts college versus a large university like Stanford. You could do grad work at Stanford.
I happen to love the Williamstown area. I visit the Clark Museum there, as well as MassMOCA and have often stayed in the area. I remember a morning having coffee in the small downtown and loving the vibe. But that’s me.
If Willliams is free I would go for it!
ps check out who teaches classes- chances are grad students do some of the teaching at Stanford, especially sections; you may have more contact with professors at Williams. I am speculating but for me, that would be something to look into.