There is a lot to see in Vancouver and it is definitely worth the trip. Stanley Park and the Vancouver Aquarium are both fantastic. If you can do a day-trip to Whistler, it's also wonderful even in the summer.
However, I would suggest visiting Victoria on Vancouver Island, instead. Victoria is absolutely beautiful, has wonderful restaurants, some fantastic parks (Butchart Gardens is a must-see!) and many attractions (it is the capital of British Columbia). Victoria is also very easy to get to from downtown Seattle - the Victoria Clipper (a passenger ferry) and the Kenmore Air seaplanes both travel direct from downtown Seattle to Victoria's inner harbor (downtown). To travel from Seattle to Vancouver, you have to travel by road and go through the land border crossing, which takes a bit longer and requires a car.