My favorite thing to do in Vancouver is biking around the sea wall in Stanley Park.
We've also done the Capiliano Suspension Bridge park and Grouse Mountain (I think these are worth doing if you've never done them before with the caveat that the suspension bridge gets crowded by late morning).
If you've never been to British Columbia (BC) before and you have the time, I highly recommend taking some extra days to explore some of the attractions outside of greater Vancouver. In my opinion, BC is one of the best (and most underrated) North American tourist destinations, especially during the summer.
For example, for our upcoming trip this summer, we're planning to spend six nights in BC pre-cruise. On the morning of the first full day of our vacation, we plan to bike around the Stanely Park sea wall. Next, we plan to go up to Whistler for two nights (the drive between Vancouver and Whistler is among the most beautiful in North America) during which time we plan to rike the Peak-to-Peak tram (and perhaps do a few other things in the area). After Whistler, we plan to take the ferry over to Vancouver Island and spend two nights in Victoria, during which time we plan to visit Butchart Gardens, which is among my favorite places in the world. After Victoria, we plan to take the ferry back to Vancouver and go to Fly Over Canada the night before the cruise.