I've heard New Zealand scenery has a lot in common with BC, so I understand your perspective; when I travel I want to see things I don't have at home!
Victoria is a good trip for a few days. Take one day for the Royal BC Museum, the legislature, and walking around downtown; don't miss Munroe's Books, a popular independent-owned local bookstore near Government St x Fort St. Virtually everything on Government St between the Empress Hotel and Fort St is a tourist trap, so ignore the shops there. Pagliacci's is a great Italian place with creatively named dishes and lots of atmosphere; I recommend it for lunch or dinner, but you'd have to eat outside of the main lunch and dinner hours because it's extremely popular.
Even if scenery isn't a priority, one of the best things to do is walk from downtown to Fisherman's Wharf, then to Ogden Point, along Dallas Road, and back to downtown through Beacon Hill Park. Fisherman's Wharf, to the west of downtown, has neat houseboats and a good fish & chips place called Barb's; There used to always be seals hanging around Fisherman's Wharf in the water, waiting for people to feed them fish, but I haven't seen any the last few times I've been there. The section of Dallas Rd from Ogden Point to Beacon Hill Park is lovely on a clear day, with a view across the sea to the mountains, and Beacon Hill Park has flower gardens.
On a second day in the Victoria area you could check out Sidney(it has some very good art galleries and bookstores) and go to Butchart Gardens. Butchart's is expensive but the flowers are very good, and if you can catch a fireworks performance in the summer (weekends July and August generally) it's quite worthwhile.
If you're here July 1 (Canada Day) there will also be fireworks downtown that evening.
Similarly depending on whether money is an object, whale-watching (mainly for orcas; if you get lucky you could see humpbacks as well) out of Victoria is a good option; in addition to the whales you generally see sea lions, and seabirds like cormorants.
If you want to see animals, urban deer are to the point of becoming a problem here (they eat people's gardens); if you head up to the University of Victoria grounds in the evening, for example around Finnerty Gardens, you've got a decent chance of seeing some.
If your family enjoy cycling, there are some good trails in Victoria (the Lochside Trail out to Mattick's Farm, which has shops and ice cream, and the Galloping Goose out to Hatley Castle on the Royal Roads University campus are both good rides; each about 10km out, 10km back). But the best thing you can do in the way of cycling is the Vancouver Seawall, either just around Stanley Park if you want a short ride (~10km?), or all the way from Stanely Park to the University of British Columbia Campus if you want a longer one (~25km). The trails are mostly flat.
Dress for hot weather - we don't usually get so warm, but this summer and the last it's been up to 30ºC fairly often, which is a real change.
An additional option is to take a day to go to Saltspring Island (there's a short ferry from Victoria), which has a good farmer's market on Saturdays in the town of Ganges, and a lot of little shops, and nice park called Ruckle Provincial Park.
If it gets too hot for you and you just want a day off, head to Thetis Lake; it's where everyone goes to swim in the summer. It drops right off, so it's not good for little kids, but it's good for teens.
By the way, if you're on the ferry back to Vancouver at dinnertime (5-7pm) the Pacific Buffet is very good and worthwhile. Good main courses, basic salad bar, tons of desserts.
Or, as you said you're okay with flying, a completely different option would be to fly to Calgary for the Calgary Stampede (July 3-12), which is a huge event for Alberta and basically a giant rodeo. It's not my kind of thing so I've never been. If you pick this option, give yourselves a day to head to the Badlands and Royal Tyrell Museum for dinosaurs and the kind of scenery you probably don't get in New Zealand.
In Vancouver, the can't-miss stuff - aside from the aforementioned Seawall - is Stanley Park [Beaver Lake and Lost Lagoon are good walks inside the park, in addition to the seawall along the coast] and Vancouver Aquarium; shops along Water St in Gastown, expecially the Coastal People's Fine Art Gallery and Inuit Gallery of Vancouver; Granville Island, with lots of great stores - the Eagle Spirit Gallery has amazing First Nations art - and an excellent farmer's market; and the UBC Museum of Anthropology. In a lot of the First Nations art galleries you'll notice that they also sell Maori art; I'm curious as to whether shops in New Zealand do the same and sell BC First Nations art.