There many hotels in Newcastle City Centre, with some less expensive options on Osborne Road in the suburb of Jesmond, about 20 minutes walk from the University.

The accommodation section of the city tourism website is here.

I would stay in The Royal Station Hotel in the city centre, about 15 minutes walk from the University: a hotel with a bit of character in a classic Victorian building (should be about £80 per night with breakfast). 

A cheaper option is The Jesmond Hotel which should cost around £50 (there are several other hotels with similar prices in the same street).