You might have to cab it to Robson Street - unless you are really into walking. Robson Street is a shopping mecca in itself - so you will want to conserve your energy until you get there. Terrific shops - lots of different things to choose from. And great restaurants. Pacific Center - upscale shopping mall - is also on Robson Street.
If you have never been to Vancouver before you won't want to miss Gastown.
You will be right near Stanley Park though, and, if you have a north facing room you will be looking right at the inlet and the North Shore Mountains - the birthplace of many famous people - namely me lol.
Not sure about location of your hotel, but I can rave enough about the Pan-Pacific right at the pier. If your budget allows, I would check it out. We stayed there for three days prior to our Hawaii cruise and just loved it.
We stayed at the Westin for four days this past July prior to our Alaska cruise. We had a wonderful time at this hotel. We took lots of walks in Stanley Park. What a lovely place. The concierge recommended a wonderful trip for us to Victoria and made all the arrangements. It was a great day trip. The restaurant next door, Cordeiros was great. We ate there twice. We also loved walking along the waterfront at sunset. We would return to Vancouver any time. It's a beautiful city.