Coventry has a historic centre with the ruins of the old cathedral, destroyed in World War II and never rebuilt, and next to it the new cathedral. Coventry calls itself "City of Peace and Reconciliation" because of its wartime and postwar experience. There are frequent buses to Coventry from the university.
Kenilworth Castle is a partly ruined castle on the edge of Kenilworth. It is the most accessible historic site in the area of the university. If you are staying in Kenilworth you can easily walk there. If you are staying in the university, take a number 12 bus.
Warwick Castle, unlike Warwick University, is situated in Warwick. It is more expensive to visit that Kenilworth Castle, and more touristic. It has large and beautiful gardens on the banks of the River Avon. Warwick itself is a pleasant small town with many historic buildings, and many restaurants.
Oxford is 49 minutes by train from Coventry. You can visit some of the old colleges, and there is a very fine art museum, the Ashmolean. Trains leave Coventry at 25 minutes past each hour. For the return, trains leave Oxford for Coventry at 36 minutes past each hour, until last train at 22:30.
Stratford upon Avon is 15 miles from the university, and can be reached by bus from Coventry and Kenilworth. It is also very touristic.