The closest to the UofR, and most convenient are all of the apartment complexes off of Elmwood Avenue about a mile down the road which the UofR bus runs.
What you haven't expressed is what type of apartment you are looking for; an apartment complex, an apartment in a multi family home, number of beds/baths, central air, laundry on the premises etc.
Utilities included. All of these factors into what will be best for you. Price range?
The UofR has a housing website.