Great location! I live about 10 blocks from there.
I would recommend taking the SeaBus across to the Lonsdale Quay - it's a very fun place to wander around, eat, and buy some cheap groceries or snacks or souvenirs. They have farmers markets, but I'm not sure which days. They have a very good fresh-made chocolates place that I try to avoid due to cost and health, but I definitely stop in once or twice a year.
You know the path around the perimeter of Stanley Park? it continues on both ends, so you can extend that and see a lot more of the downtown area. I'd recommend a bike for this. My boyfriend and I do a really nice circuit from Gastown (where we live) through Coal Harbour, around the park, continuing along past Sunset Beach and English Bay, through Yaletown, and up through Chinatown to get back home. It's completely on bike paths, no cars to be seen, and 90% right next to the water - all around gorgeous ride, especially in this weather. Hit me up if you want to go together (this applies to anyone else in Vancouver as well, not just OP!).