The weather this week is supposed to be beautiful so pretty much anything you do outdoors should be great.
Where are you staying ? I'm a local (and was in Tourism for 15+ years not so many years ago) so would be happy to pass on a few suggestions (restaurants, shopping etc) close by where you are staying if you would like.
When the weather is nice a must do is Grouse Mountain (go to google images and type in "Grouse Mountain Vancouver"). The Gondola ride up the mountain and the panoramic scenic view of the City is spectacular. There are "tours" to Grouse but it's relatively easy and inexpensive to get there on Public transit (take the Seabus from downtown over to North Vancouver and then take the Grouse Mountain bus that's waiting at the bus loop on the other side). The Translink website which has all the schedules and route planner help (which buses to take) is found here :
http://www.translink.ca
Most of the local attractions mentioned so far (Stanley Park, Gastown, Granville Island etc.) are probably easiest and best accessed by tourists on one of the local hop-on hop-off city tours. There are a couple of companies in town that run buses around a circuit continuously throughout the day. The cool thing is you can hop on and hop off where you please and pick up the next bus that comes along and continue on. The oldest and probably the best is run by the Vancouver Trolley Company :
http://vancouvertrolley.com/tours/hop-on-hop-off . Looks like they have a special on right now where you get a 2 day pass for the price of one. It is a tour so while you are on the bus you are getting commentary on what you are seeing go by.
As mentioned Victoria and Whistler are fabulous suggestions but only if you are willing to give up an entire day to do one of them. Victoria (and especially the ferry ride over to Vancouver Island) would be gorgeous at this time of year when the sun is shining and the Butchart Gardens (one of the highlights of a Victoria tour) would just be coming into bloom. If you think you may want to do one of these tours I would highly recommend these folks :
http://www.vancouvertours.com.
Food suggestions : Vancouver has easily some of the best Sushi, Chinese, East Indian and Seafood restaurants of anywhere you could visit. If you are staying downtown make sure to check out one of the local food trucks for lunch. The food that some of these street vendors are putting out is amazing. Locations of the trucks can be found here :
http://streetfoodapp.com/vancouver . In case you're not sure what I mean by food truck :
pm me if I can be of help