Lots of great hiking on the north shore. Avoid the grouse grind though - unless you like humanity-infested, litter-laden stair climbing. Lynn Valley has a lot to offer for exploring and reasonable hiking with great views. Not the Rockies, but well worth it.
Broadway between MacDonald and Alma St. is really nice for strolling.
As someone mentioned, check out QE Park. Really gorgeous there.
Commercial Drive. Grab a slice of pizza at Uncle Fatih's on Broadway at Commercial, then stroll down Commercial Drive, check out the pubs, shops, and Italian people. If it's the weekend, head over to Latin Quarter restaurant, which turns into a salsa bar at night. Libra Room has live jazz every night - well worth stopping in for a couple.
Take what people say about Hastings with a grain of salt. Their comments are much ado about nothing. Hastings has some great, lively, youthful bars, pubs, and music venues. Old dive bars like the Astoria, Pat's Pub, Waldorf, and Funky Winker Beans cater to younger crowds on many nights thanks in large part to the cheap drinks. I've had many a good night at these places, whether it's a punk show, karaoke, or whatever. Hastings has some of the best pubs in Vancouver.
Check out Gastown as well. It's got a little bit of grit that bleeds over from Hastings, but it's a bit more upscale. Bars like the Blarney Stone, the Cambie Hostel Bar (wait, did I say upscale? yeah, nevermind that), the Met, etc., are always packed and you'll meet plenty of fun people.
Wreck beach is, hands down, shorts off, the best beach in the city. It's beautiful.
Kits is nice for hilly strollng.
I like Main Street a lot as well.
Take a bike ride around the Sea Wall, which circles downtown and goes all around Stanley Park. What a collection of views! My favourite part of Vancouver. Incredible.
So yeah, there's quite a bit that's worth your time. What a city.
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