I'll chime in here, as a long-term resident of Victoria!
Your basic neighbourhoods around UVic are Gordon Head and Cadboro Bay. McKenzie Ave runs straight into campus, and there are a handful of buses that run along that road or roads that intersect - such as Shelbourne and Cedar Hill. If you're looking for beaches and walking distance to UVic, Cadboro Bay or Gordon Head Rd. are great options. Good luck finding something in those areas though, places go quick and are usually on the more $$ side!
If you are sad about not being able to live on the beach, Gyro Park is just down the road from UVic (about 20 mins walking) and has a lovely beach for naps and happy hour.
If you don't mind more of a bustle, Shelbourne Rd. has lots of stuff (fast-foodie style restaurants, a few banks, a pet store, yoga studios, etc.) and a pub. If you like malls and want to be close to a massive Canadian Tire, the area around Hillside Ave (dubbed Oaklands) is decent - and the #4 bus runs right along Hillside to UVic.
Oak Bay is a bit too far for a walk, and the buses kind of suck, but if you're a cyclist or have a vehicle it's a gorgeous area. Lots of old rich white people though, and rent is a little pricier.
The area between McKenzie Ave and Lambick Park tends to be packed full of undergraduates living off campus for the first time, so it can get pretty rowdy, if that matters to you.
Downtown is definitely an option, if you're into the big city living. There are several buses that go direct to UVic or connect along the way. James Bay used to be a pretty sketchy area but it's getting fancier. Esquimalt has been described as the Surrey of Vancouver Island, but it's also getting a bit fancier. They even have a Red Barn now, which is a really important place for ya'll to visit because the SANDWICHES, OMG. But you'll be adding some transit time if you head across the bridges to Esquimalt/Gorge.
Then, of course, there is Langford/Colwood/Metchosin/Sooke... Like rkathleen said, I'd avoid that area. Lots of people are buying out there because it's cheaper but the Colwood Crawl is a huge line of traffic that's super uncool and inconvenient. Oh, and the Uptown area - again for those who love malls. Uptown (funk you up) has a Walmart and a Whole Foods and a Cupcakes (super critical) and is pretty decent for buses. Mayfair Mall is down the road and just got a facelift and has a Sephora, Chapters, Aritzia, and some other less important stores. There tend to be apartments in those areas.
No, we do not have an IKEA.
If you're more of a small-town person (hehe) and have a vehicle - heading up the peninsula is a lovely option (towards Sidney). There is definitely less to do but lots of farmland and horses and stuff. I've seen a few places available around Elk Lake too, which is about 10km's around and great for dog-walking/training for marathons/solitary walks while listening to Nickelback.
Anyways, if you have any questions, as the others have said, feel free to send me a message!