Go to Richmond and toss a pebble in any direction… any place you hit will surely be an authentic Chinese restaurant! If you do make your way to Richmond, try Aberdeen Center. The shops are sort of “Hong Kongy”, there’s a play area for kids, and people are always raving about the $2 items at Daiso.
I’d also recommend you take a look at Main Street, going up from about 49th Ave all the way out to Broadway or so (Broadway is essentially 9th Ave). It’s adopted the nickname “Little India”, so if you’re looking for something a little more multicultural, it’s a good area to take a stroll. I’d also recommend Commercial Drive for the same change-of-scenery experience, BUT Commercial Drive isn’t all that kid friendly.
If your family isn’t into too much shopping, try taking them to The Hillcrest Pool. It’s basically an indoor water park for the kids (and adults!) to play around in. It was the curling rink during the Olympics that they converted into a pool. Pretty cool to check out just for the history factor.
If you have the time and the kids are okay with it, try visiting the Capilano Suspension Bridge. It’d be a great experience for your 10 year old. ETA, the Lynn Valley bridges are also pretty awesome, but it’s a little more complicated to figure out how to get to, especially if you’re not familiar with the area.
For something a little more bland, do a picnic at Stanley Park. It’s where the aquarium is, and it’s quite a big park, so you can actually make a day of it. If you go there, take a look at the totem poles… apparently, that’s what all the tourists end up doing!