Welcome to Vancouver!
That south Vancouver Mark's/Best Buy lot is huge but if it's raining at all only the loading bay area is dry, and it's become a virtual skatepark these days, as far as the number of people there. I used to live a block away before it blew up and we always had it to ourselves back then. Still, people bring obstacles to skate so if you can deal with a crowd it's an option on rainy days. There's a bump over sidewalk in there too but again, only really good if it hasn't been raining hard. The loading bay part is always dry.
The Art Gallery/Law Courts underground downtown has been the go-to since at least the early 90's. Hit and miss as far as security is concerned. Half are totally cool with it, the other half are grumpy old farts who complain that you made them "walk a kilometer". Sometimes I just say I'm gonna leave and then stick around and never see them again anyway. It's mostly manual pads but there's a couple curb cuts, a rubbermaid can, and a long section of waxed curb against the wall.
There's other covered lots but no one wants to blow out the limited spots we have so you'll have to do the searching on your own for more than I've provided above. I'd suggest just poking your head into any covered lot you come across whether you have your board or not.
I've heard talk that the rather tight spine mini ramp is returning to Granville Island this year. That's another option, though I never hit it up when it was there before due to crowds.
Plaza will have dry strips if it hasn't been raining hard, but it's also incredibly rotten when it's wet in there and takes a while to dry due to all the divots in the ground. The granite got replaced last year though, so that's a bonus. Nice long slabs too. They somehow fucked up and forgot how to build skateparks when they did the renos, leaving gaps between some of the granite pieces, but I think they're doing ok now.
All of the schools in the lower mainland are being rebuilt since they're mostly 100+ years old, which so far has resulted in a lot of new spots. They've got countless schools to go still so you moved here at a great time - Vancouver has never been so blessed with good street spots as it is right now.
If you don't own a bike, buy one. This city is perfect for biking around to skates spots.
The rain is really hard to get used to, but once the borders are open I suggest doing what I do and escape to California each year for as long as you can afford in the winter. It helps immensely.
Have fun!