Kim is correct in that there is not one particular zip code that pertains to the University area. 72701 is south of North Street, and 72703 is north of North St. Both may have properties within walking distance of the University. The other possibility is to purchase a property that is on one of the University Bus routes. This will increase the number of possibilities for you to consider. Below is a link to the page on the U of A website that shows the bus routes.
I also have a property listed on Leverett. 2 bedroom/2.5 bath condo. On the Blue Route (bus stop is almost in front of the building). MLS number is 528628.