Whistler is stunning in the summer, with all the usual resort activities: ie, swiming, golf, horseback riding, biking, etc. You can take a ride to the top of the mountain, and from there either do some alpine hiking or just take in the amazing views. There's also sort of a water-luge thing at Blackcomb. I enjoyed just hanging out at one of the lakes.

On the other hand, Vancouver is pretty damn spectacular in June, also. If this is your family's first or second trip to the city and/or you're only there for a few nights, I'd stay put. On the other hand, if you've been to Vancouver a lot and are staying at least a week, it's well worth the (long, but pretty) drive up for a night or two at Whistler.