Where to start ...
There are a lot of breweries in Vancouver. Most of them are located on the east side of the city -- many clustered around Grandview, Strathcona, Powell Streets. The Main Street area is another cluster. Am guessing that you'll be staying downtown; if so, it's an easy bus or train ride to many of them. My recommendations are Brassneck (excellent), Strange Fellows (great standards and sours), Callister (multiple brewing companies brewing out of one brewery), Bomber (my favourite pilsner) and Strathcona (good selection of tasty beers and pizza). You could ambitiously walk through Grandview/Strathcona or Main Street from one brewery to four or five more. It's pretty great.
If you're looking for a bar with a good selection of local craft beers, St. Augustine's in right next to the Commercial-Broadway Skytrain station. Best part -- hop the train from downtown, have some beers and train back DT. If you're wanting to stay downtown, the Alibi Room is the gold standard for a craft beer pub.
Plenty to choose from. Do your homework on what styles you're looking for and you'll be spoiled for choice.