Vancouverite here.
Whenever the missus and I think about short road trip (ie weekend/long weekend or even a daytrip), we always say, "North, East, South, or West."
North kind of means Whistler for us but there are different iterations and stops. A simple trip is up to Whistler and back along the Sea to Sky Highway. Amazing views, at least during the first part of the trip. Lots of places to stop like Squamish as mentioned (which kind of has an interesting food and craft brew scene) and other touristy places like Shannon Falls, Britannia Beach/Mines, the Sea to Sky Gondola (which is kind of integrated with some nice trails)/the (Stawamus) Chief, etc.
A different circuit we do is east and then north via Highway 1, turning around at Lilloot, and then back down the Sea to Sky Highway (along Whistler, Pemberton, Squamish, etc). It's a long daytrip. Along Highway 1, you pass by a lot of somewhat interesting small towns, the touristy Hells Gate tram, Lytton which unfortunately burned down due to a fire and hasn't been rebuilt yet and is/was frequently the hottest location in Canada in the summers, etc. You're driving along the
mighty Fraser River which is pretty scenic. We've run across mountain goats along the highway a few times.
East for us means the Okanagan/Kelowna and wine country via a long weekend trip. We'll typically start off on Highway 1 and then divert to the Coquihalla Highway in Hope. (Fun fact: Much of Rambo First Blood was filmed here.) Personally, I think the drive from Vancouver to Hope is overall boring with only a few interesting views sprinkled in. Whereas along the Coquihalla, you're heading up into the moutains and then back down into Merritt so the views are kind of nice. In Merritt we'll veer east the rest of the way to Kelowna.
On our return trip, we'll head south, running along Okanagan Lake, though Penticton, and if we have time, all the way down to Osoyoos which has the distinction of being the only desert in BC. We'll then head west back to Hope and onto Vancouver along Highway 3. There are a lot of small towns and quirky towns like Keremeos along the first part, many with cute fruit stands. And then you'll pass through Manning Provincial Park which is a large recreational area with trails, fishing, kayaking, etc.
If you keep heading north at Merritt, you'll reach Kamloops which is a nice city along the Thompson river. We've been able to do a day trip to Kamloops and back to attend fan day for the local professional football team's (BC Lions) training camp. Very long day though.
We've also done all the way east to Alberta along a circuit with stops in Jasper, Edmonton, Calgary (Stampede time in July), and Banff over the course of about a week. Lots of driving of course. There's also a bit of a hotsprings subcircuit if that's your thing.
Watch for speed traps.
South means heading to the States for us: Bellingham, Seattle, Outlets, etc of course. Just for our daytrip tolerance context, we've done daytrips to Seattle and that's likely the furthest south we'll go for a daytrip from Vancouver.
West means the Sunshine Coast, Gulf Islands, and Vancouver Island with the added cost of a ferry of course. Beyond the places you've mentioned, we'll do a long/four day weekend trip to Tofino on the west side of Vancouver Island. You take the ferry to Nanaimo mid-island as mentioned. I find the drive a mixed bag. Some parts are interesting: Windy roads, nice views along lakes and forests (eg Cathedral Grove), while other parts are kind of a grind. You pass through Port Alberni which is kind of a resource town that I don't find too interesting. One route passes through Coombs which is another small quirky town with a fun destination-kind of market with "goats on the roof."
Personally, I think it's quite the effort to do a daytrip to Vancouver Island (with the Gulf Islands only slightly less so) because of the added complexity of taking a ferry (or one of the other options like float-plane, downtown-downtown passenger ferry, etc).
