Exeter isn't too expensive, compared to other areas like London or Bristol, but it's not as cheap as in the north. The average student rent is between £50 and £70 (about $100 - $140) a week per room (which may or may not include water, gas, electricity - usually not), but you do usually need student ID (which may have to be an Exeter ID) to get a room in a student house or flat - otherwise you'll have to pay the higher non-student rates'.
I would avoid letting agents (for example, Cardens is one to stay away from) that try to charge an administration fee (about $60) and you might be better off asking the university for their private housing list. Every year around Jan - Feb, they release a document containing all the houses and landlords in the private sector that rent to students and who are approved by the university -
www.studentpad.com . This is a safer method to use (if it is suitable for international students, that is) as you can avoid unreliable and irresponsible landlords who will try to get away with charging you a lot of money and don't get things fixed when they are broken!
Looking at the Exeter Uni website, it seems that they can only guarantee accomodation for unaccompanied international students, but I think the accomodation office also deals with private rented accomodation. Also, the student's union (the Guild) has a site intended to help with finding private housing -
http://www.guild.exeter.ac.uk//helpandadvice/adviceunit/housing which may be of some help.
My feelings of Exeter now? It's a lovely city and a beautiful campus and I enjoyed my time there, but if I'm honest, the best part was the year abroad. I enjoyed it so much that I've actually applied to do my PhD at the same university in the US. I studied at the University of New Mexico in Albuquerque and it was the best year of my life - I spent my last year in Exeter missing it like crazy, expecially the sunshine!
One little thing about Exeter is that you will always need to carry an umbrella with you - it often starts raining with no warning (which apparently is the reason why the university grounds are so green) and being caught without an umbrella is really annoying, so it's a good idea to always have one handy. It was difficult to get used to again after spending 10 months in a state which gets 330 days of sunshine a year!
By the way, what will you be studying at Exeter?