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I will talk about some options from least accessible to most:
Mt Cheam. It's in Chilliwack, and you need a pretty capable vehicle to go up the rough logging road leading to the trail head, but wow is it worth it. In the top three most beautiful peaks I've done in the lower mainland
Garibaldi. It's a bit of a drive also, but awesome. You can chill around the lake areas or do the Tusk if you're feeling ambitious. However expect it to take up all day, if you go at a leisurely pace it's better done in 2 days.
The Chiefs near Squamish. These are pretty legendary and worth doing. This is more laid back and easier than the aforementioned hikes, but this also means more crowds. Make sure to do all three peaks instead of just the first, as the first is actually the worst one.
The Lions, Mt Brunswick, or Mt Harvey on the North shore. I've only done the lions, but they're all great peaks. Unfortunately the trail head for all of them is in Lions Bay, a pompous little community, and parking is usually limited. There's probably still a lot of snow on these mountains this time of year
Grouse mountain area. There are some lesser known peaks around here such as Goat and Crown mountain. I'd call them medium difficulty
Lynn Valley area. This is more of a chill nature walk than anything, unless you want to do something like Mt Coliseum, which is pretty long. There are some cool waterfalls and bridges around there so it's pretty nice.
pic is from Mt Cheam