St Ignatius College Prep is essentially within the UIC campus and is where the UIC teams train. Unfortunately, that track is not always open. I trained there last spring by getting permission from the UIC coach to be on the track while their practice was going on.
Other than that, there aren't many tracks. if you have a car, you could get up to north park college (kedzie and argyle) and use theirs. there is also a bad track near north and clybourn and a rectangular one at northwestern's law/med school campus.
Indoor tracks are even tougher; there aren't any nearby at all. the university of chicago has one, but you need access to their fieldhouse to use it and it's way down in hyde park. (for the record, there are two outdoor tracks down there. one on the UofC campus, and a really nice public one smack in the middle of Jackson Park.) Additionally, some high schools (but not many) have indoor facilities--proviso west comes to mind--but none that i know of are nearby and have easy public access. as far as i know, none of the other colleges in the city(north park, depaul, loyola,...) have indoor tracks either.
I was living out in wicker park last year and working at the UIC medical center. doing workouts on tracks was inconvenient at best. i moved to california last month and now live within two miles of at least three tracks. such is life.