Well lets see here...
If you get a chance to hit up Whistler for a weekend, definitely do that. Its expensive up there but definitely worth going up there for a few days. Lots of things to do up there even in the summer. My favourite is ATV'ing in the summer in the mountains. Really fun.
Definitely hit up Vancouver Island if you have some free time. Lots of outdoor things to do and places to see. Its beautiful out there.
Another really awesome trip to make within BC is to head up to the Okanagan Valle and check out the surrounding area's including Kelowna. Very-very nice up there especially during the summer.
Another really cool trip is to take the train trip to Banff into Alberta. Very scenic.
^^^ Those would be suggestions for trips travelling to places within B.C. for a weekend or something like that.
In and around Vancouver and the lower-mainland area where I guess you will be staying there is a sh^t ton of stuff to do and places to check out...
Definitely check out North Vancouver and what it has to offer... Grousse Mountain, Mount Seymour, Capillano Suspension Bridge.
In downtown Vancouver... just too many places to list off really... Lots of 2010 Olympic sites you can see, check out the walk along the seawall, science world, stanley park is a big favourite of tourists. Oh and three beaches in that area that are really awesome Jericho Beach, Spanish Banks & Kitslano Beach. If you only go to two I would visit the latter two.
Obviously downtown Vancouver has the usual really cool bars, museums, etc. to visit. Yaletown downtown Vancouver has a lot to offer.
And then there are all the surrounding cities outside of Vancouver in the lower-mainland and what they have to offer. "Downtown" New West Minster is pretty cool... a couple nice casino's as well. And thats just one of many places surrounding Vancouver.... Burnaby has Metrotown Shopping Centre, Whiterock is one of the coolest places in the summer IMO to visit... the strip on Marine Drive is filled with tons to do and then of course there is the awesome beach there as well.
Thats just what comes to mind right now... lots of more places and things to do that I probably haven't thought of...
Sorry for the poor grammar I was trying to just get the idea's out of my head and typed.