Best Cities for Mathematical Study This may sound silly, but... Suppose an aspiring amateur mathematician wanted to plan to move to another city...
What are some cities that are home to some of the largest number of the brightest mathematicians? I'm sure this may depend on university presence, or possibly industry presence, or possibly something surprising. Wondering where the best place to take a non-faculty job at a university and try to make friends with some sharp minds in the computer lab or at the nearby pub might be.

Without sounding biased in any way, I would say Cambridge/Boston is a good choice for you. In the particular order of funded research/department size there is Harvard University, MIT, Boston University, Boston College, Northeastern University, Brandeis University, Tufts University, Bently University, University of Massachusetts at Boston, Curry College, Eastern Nazarene College, Pine Manor College, Hellenic College, Lesley University, Wheelock College, Lasell College, Simmons University, Cambridge College and Bunker Hill Community College (and many, many more) within the metropolis. See http://en.wikipedia.org/wiki/List_of_colleges_and_universities_in_metropolitan_Boston for a complete list.
A number of these institutions offer extension programs (with open enrollment and classes in the evening or weekends) suitable for life-long learners and aspiring amateur mathematicians. For example, the Masters for Mathematics Teaching Program at Harvard University offers courses in all major mathematics subject areas, taught by many instructors which hold separate positions in the university (like adjunct/junior faculty, preceptors, senior lecturers, post-doctoral or teaching fellows and even a senior graduate student).
