Most Nobel Prizes (per "unnoficial" counts that have some weird inflation for some universities but not Chicago!):
1. Harvard
2. Columbia
3. Cambridge (UK)
4. Chicago
5. MIT
6. Berkely
7. Oxford (UK)
As for Chicago -- well, when I asked Irving Kaplansky to volunteer something I might not yet know, he told me the history of the department. That didn't impress me. I eventually picked Harvard over Chicago for several reasons:
-- Chicago had a fixed course curriculum. Harvard had zero actual course requirements. -- Harvard's faculty seemed more approachable by and engaged with the students. -- I was more attracted to Harvard's resources in other departments. (And in fact, I wound up post-doccing at Harvard in public policy.) -- Cambridge was a lot nicer area to live in than the area around University of Chicago.
I made the right choice. But I surely would have been happy with Chicago as well.
1. Cambridge (UK)
2. Chicago
For example, several years ago a couple friends I knew withdrew their undergrad applications to Harvard when they were granted acceptance to uchicago because of the mathematics curriculum (it wasn’t an objective choice necessarily, but it was a well thought out one that was academically motivated).
It was a little odd that its graduate programs were almost universally held at the pinnacle of academics, while most people didn’t think the undergrad was that good. That changed when uchicago accepted the common app (looks more selective) even though the rest didn’t change as much. Suddenly it skyrocketed in the rankings. It was always that good, though.