That's a pretty big "may", since there's pretty much zero evidence that spending on stadiums brings in enough revenue to offset the cost of building them. I'd rather they ditched the arena idea entirely and built the area up with housing and some shopping. That would certainly have much more of a benefit for the city than building a giant arena that'll be empty for most of the year.
My wife and I just bought a new house in Westboro a few months ago, so I can vouch for the neighbourhood being awesome. It's one of the more expensive parts of the city (we could only afford our house because it's right on one of the main streets, plus it's almost 100 years old), but I think it's worth it. It's not too bad if you don't drive -- there's good bus access, and some pretty good shops. Where were the apartments you looked at?
In terms of house-hunting, the market is pretty dead at the moment. The busiest time of the year is May-June, so if you want a decent selection from which to choose, you'll need to wait a few more months. It's definitely more expensive if you want to live inside the Greenbelt, but it's doable if you're persistent. (Vanier is super-cheap, though I'll have to go against what everyone else here says: it's a terrifying, crime-ridden hellhole, relatively speaking.) I don't know what your feelings are on agents, but it's possible to get by without one -- Grapevine and Kijiji usually have a good selection once the market gets going, but be warned that people usually set higher prices there than they can reasonably expect. (We bought our house from a Grapevine seller, but we had an agent, so it was like the best of both worlds.)