OK, since you're in Seattle, you know what to expect weather-wise. Since you have kids, my first suggestion would be, like Kari said, the aquarium! It's wonderful. Qila (one of our belugas) had a calf, Tiqa, fairly recently and Tiqa is still pretty little, which is neat to see. Her grandmother Aurora is pregnant right now. The whales are wonderful. There's a new jellyfish exhibit too which I haven't seen yet but which is supposed to be amazing. You'd want to budget at least half a day for the aquarium, especially with littles.
Chinatown, hmm. I love it but I don't know if kids would. It's not really touristy, and it butts right up against the worst corner in the Downtown Eastside (http://en.wikipedia.org/wiki/Downtown_Eastside), which is the poorest part of Canada. I don't think the DTES is a dangerous place (I do most of my grocery shopping there etc.) but it's not pretty and not pleasant, so it's not surprising that Chinatown's also pretty crowded and gritty. There are some great restaurants (especially Phnomh Penh: http://www.beyondrobson.com/re....._the_trip/). There are lots of interesting groceries, bakeries, etc. and the Sun Yat Sen gardens are great, but you would probably enjoy it more without kids.
Grouse Mountain's OK but a bit expensive for what you get. They have some grizzlies up there in an enclosure which would be neat for the kids, and of course the gondola is fun. If you have a car, the suspension bridge in North Vancouver in Lynn Valley Canyon park is beautiful, fun and free, unlike the Capilano Suspension Bridge. It's a great park for kids and you could easily do a short walk or a longer one. http://www.dnv.org/ecology/see_do/see_do.html
I heart Granville island; try to come during the day on a weekday, because it's a zoo on the weekend. Some of my favourite food things there are the spinach and feta-stuffed bagels at the bagel stand, cheese from Oyama's stand, donuts or giant apple fritters from the donut stand, and coffee from JJ Bean (all in the public market), plus beer from Granville Island Brewery. If you come to Granville Island you shouldn't miss Gravity Pope (http://www.gravitypope.com/) or Spank Shoes, which are both on West 4th a 2-minute drive or 10-minute walk from Granville Island. And of course since you're staying downtown you'll be close to Pacific Centre, which has Holt Renfrew and H&M. You should also check out MEXX on Robson if you have time b/c I don't think you have one in Seattle, as well as Plenty.
As for veg restaurants, sushi and Asian options abound. I adore Banana Leaf especially (http://bananaleaf-vancouver.com/, the one on Broadway at Bayswater, in Kitsilano, is the nicest), and Peaceful Restaraunt or Sha Lin Noodle House (http://www.beyondrobson.com/re.....le_action/ both are cheap and are a couple of doors away from each other) which make noodles by hand right in front of you. THE classic place, though, is The Naam. http://www.thenaam.com/naam/ You HAVE to go here, it's quintessential Vancouver and it's kid-friendly, too--but get there early or expect to wait in line for a while. Try the oven fries with miso gravy, the Thai Noodles, the croissant melt, or the enchilada thing with avocado and cashews. Or go for brunch! They have the best brunch. If you drink beer, they sell Crannog's organic Back Hand of God Stout. Also, the amazing cheese store Les Amis du Fromage just opened a wine and cheese etc. place called Au Petit Chavignol. Not sure how kid-friendly it would be. Another fun option near Granville Island and Gravity Pope is Las Margaritas--fun, relaxed atmosphere, lots of variety on the menu (they can make a lot of their items veg), kid-friendly. http://www.aupetitchavignol.com/ and http://www.lasmargaritas.com/.
Let me know if you have any more specific questions or whatever.