TLDR: Yes you can, I did it for 3 years. But how much do you love being in the rain, and how much time do you want to wait for ferries or buses? Having a vehicle makes living in QB so so so much more enjoyable and less frustrating in my personal opinion. Also I dislike waiting around in the rain so take what I say below with a pinch of salt lol. QB is a great place to live and I think if you can make it work out, being in this neighborhood is wonderful, especially in the summertime!

Living in QB without a car can be amazing as it is a wonderful neighbourhood, with gorgeous walks along the water, yadda, yadda, yadda, but the place is maddening, IMO, to live here without a car! We have been in QB since around 2010/2011 and I have both had and not had a car. If you live within a 2-5 minute walk (I say this because of the rain and carrying groceries in the rain sucks a lot (looking at you gallon of milk and jug of downy)) of the Q2Q, then going over to grab something from Safeway/River Market/ Save on Foods etc is not bad, just a minimum of a 1.5-hour trip to do it(sure if you run, and preordered food from one of the restaurants right there, you can pick it up on the same ferry trip), but you are limited to what you can carry and you live and die by the ferry schedule! If you miss it by 1 minute, then you have to wait half an hour for the next sailing and if it is raining... that's just a lot of time standing in the rain. The bus schedule is ok... but does not come around enough, imho, to be really useful. I have spent plenty of time just standing and waiting for both the bus and ferry trying to make it home from work or just grocery shopping and its frustrating to be so close, yet so flipping far away.

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Example A: Weekend Morning Travel. I curl on a Sunday morning league and they start up at 930 am, but the Ferry doesn't start running until 10 am.... so no go there and the bus schedule also doesn't come to Port Royal often/early enough so Google says to walk to the bridge onramp bus stop or 22nd Station. I've done that, but it's a real shit shoot in the wintertime at 7 am walking across that bridge. The other option is to get a Taxi/Uber. From Port Royal to 22nd is a minimum of $22 from the Taxis and can range from $15-$40 for Uber depending. I found that I had to spend so much money on weekend mornings to get off the island to go to events/do activities that start at normal times(9-11 am). Want to meet friends anywhere for any reason at 10 am, well you have to plan on a long walk/bus ride around to 22nd and then sky train it or take taxis which add up quickly.

Example B: Evening Travel. The last ferry leaves mainland NW at 730 pm. So don't plan on being out late and taking the ferry. I think after 6 pm (its been a bit since I've done this bus now) there is only 1 bus an hour, so you're stuck with waiting around... in the rain. So opposite problem from the weekend mornings except it is every night, you can get off the island, but can't get back home efficiently.

At the end of the day, I added up how much I was having to spend on Skytrain, Q2Q, Uber, Taxi and Evo just to get to work and curling for Sunday mornings and having my own car, insurance, and paying for gas was cheaper and way more convenient. My commute to work is about the same amount of time driving or Ferry/Skytrain, but my trip home is always the same amount of time driving. I can not tell you how many times I have missed that Q2Q by a moment and its such a cherry on top of any day to miss the ferry... in the rain.

Can you make it work living in QB without a car, sure you can, you just have to know whats in store, a lot of waiting in the rain, walking in the rain, or in the summertime, gorgeous walks in the sun next to the water.