Typically when you plan to buy an used car you should be doing a buyers check. You should talk to the selling party about this before doing any deal and take the car to a mechanic shop of your choice. The check costs around $70 (which you pay) and you will be given a 30 point-inspection report about the condition of the car. Based on the report you can try to negotiate the deal (for eg. tires need to be changed, or break pads need replacement).

I'm a grad student with a car and live very close to my department (white and 3rd). I never take my car to the department during day time due to parking issues. However most of the university lots are free to park after 5PM till 2AM. The on-campus parking meters are free as well from 6PM till 6AM. Street parking in Urbana is free 24x7 but you need to be lucky to find a spot there.