Chinatown is great and I like the interesting contrast between the touristy, gentrified Gastown and the Downtown Eastside right next door (which is North America's worst urban slum- not dangerous, just very, very sad).
Downtown Eastside apart, the rest of downtown Vancouver is nice, you should walk around Stanley Park, go to Granville Island market, possibly Kitsilano, take the Seabus over to North Vancouver to go up Grouse Mountain and visit one of the Suspension Bridges (NB: Lynn Canyon is free and much less crowded than Capilano). Horseshoe Bay is really beautiful too.
Really though, while Vancouver is surely a great place to live, it's not exactly full of incredible tourist attractions. It's more a place to enjoy the lifestyle and the beautiful views of the mountains and sea, relax in the parks etc. Downtown is actually quite ugly in terms of architecture. If you like cheap and authentic Chinese, Japanese and Korean food then you'll love Vancouver.
Try and go over to Victoria on the seaplane if you can- it's a nice city for a stroll and the views on the trip over are beautiful. If you take the bus/ferry it's about 3 hours each way. Good whalewatching there (killer whales).
Go out whalewatching, the wildlife is incredible: tons of seals and sea lions and orcas etc. I would definitely consider going to Victoria too, it's a relatively short ferry ride from Vancouver, and it's a completely different city, probably the best example of a Colonial British city in the world.