Kitsalano is the very residential west side neighborhood JUST south of downtown. There's a pretty good chance your AirB&B will be here or nearby neighborhoods. roughly speaking, west = nicer/bougie, east = sketchy/funky. The city is very safe, esp. from an Angeleno point of view. Even the worst areas (East Hastings) are very safe during the day, and only sketchy at night if you're up for causing trouble to start with. Kits certainly has its neighborhood stuff, though I'm not terribly familiar with it. Getting downtown on transit is super easy (get a compass card at any train station or drugstore)
Make sure your AirBnB has parking included (driveway, reserved spot in building). Bring an umbrella. If it snows, just stay away. The city doesn't have the equipment to cope and loses its mind for 36 hours any time there's more than a couple of centimeters.
The West End is on the downtown peninsula and is centered around Davie Villiage, the gay neighborhood. Small but cute bars, restaurants, etc...
I wish I could be more help but I'm only just getting my bearings here myself. There's a large number of craft breweries and pubs here, so you won't be hurting for good beer. They also do a lot of vodka and gin distilling. For complicated reasons, there's almost no 'canadian' whiskey (or whisky). I was surprised, too.
If some cannuck friend of yours tries to get you to eat ketchup or all dressed chips, run. run far, run fast. They are vile and that person is not your friend.