You're partly correct with the TRACON, however TRACON controllesr are vastly different and have a much harder job than their ARTCC (air route traffic control center) or as you know them, en route or tower counter parts.
Tracons work arrivals and departures out of main class B or C airports, sometime D's however your're usually just handed off to a center.
And you dont need to be a citizen, just call up the HR department of the center you want to visit a few weeks in advance, and youre good to go. I have visited many facilities in preparation of my graduation, in fact Ill be going to KSEA tower in two weeks