Hi west_0515,
I attended Exeter University for 4 years (although I spent one of those years studying in the US), so hopefully I can help you out a little
. Exeter is a pretty small city (only 100,000 people, 12,000 of which are students), so pretty much anywhere is within walking distance (not counting the residential areas on the outskirts of town)!
Most of the student accomodation is within 20 minutes walk of Streatham campus and some of the on-campus flats cater for couples (although I'm not sure if there are any restrictions for international students/spouses).
Off-campus, areas close to the university include St. Davids (down near the train station), near and around Pennsylvania Road (although this area is popular and there is competition to get housing), possibly Central (near the main shopping centre) and maybe Heavitree. Watch out though, for places near St. Luke's Campus because they can be up to thirty minutes walk from Streatham campus and also, anything down near the quay and the river are pretty far from campus too.
However, there is also a frequent student bus service from campus to various parts of town and most students do not have cars because unless you're going to be driving out of the city a lot, you won't need one.
You'll probably want to look for a small flat rather than a house because most houses cater for 4-8 people and getting one just for 2 will cost a lot of money - even an apartment within a house could cost up to £500 a month for two people.
I would recommend joining the Erasmus and Study Abroad Society (which I helped to set up in 2004) - they provide social events for international students and arrange trips to various landmarks and other cities.
The city centre is good for shopping (all the high street names, plus some cool independent shops) and for pubs and bars. The nightclubs are okay, but since Exeter is not that big, they are limited. The campus has several student bars (which sell cheap drinks) and it's own nightclub, the Lemon Grove (affectionately known as the 'Lemmy') and there are several concerts hosted in the Great Hall and the Lemmy each year, including pop/rock stars and also classical orchestras.
The university holds several balls and big events each year, including the Fresher's Ball (primarily for freshman, but I think anyone can purchase a ticket), the Law Ball, the Safer Sex Ball (to raise money for charity - anything goes at this one!), Powderham Ball (held at Powderham Castle) and the Summer Ball - an all-nighter held on campus until 6am!
I am ashamed to say that I have never even been to Torquay or much of the surrounding area, despite living nearby for 3 years and only living 80 miles away for my entire life!
Hope some of this helps.