If you know downtown already, and want to feel the West, I'd recommend scenic SeaBus trip to Lonsdale Quay.

1. Once you pickup your luggage, left luggage is just outside the baggage claim to your left. $4 per piece or something.
2. Taxi is always convenient, but public transit is as smooth unless during rush hour. Take #424 to Airport Station (5min), then #98-B to Harbourfront (40min), then SeaBus to Lonsdale Quay (10min, q15min), $3.25 all the way.
3. There's nothing upscale, but market-style dining area with seafoods, ethnic, etc. Nearby is a nice quiet bayside park, where you can stretch out a little bit.
4. The Quay is the traffic central in North Van, so you can add a trip to Capilano Suspension Bridge (#236 r/t), or stop-by at Stanley Park on the way back to Harbourfront (#242, 246 or N24 to park, then 240 to Downtown)
5. From Harbourfront to Airport, expect 50-60min, since #424 makes a little detour before arriving at terminal building.
6. Day-pass is available $8 at 7-eleven, on your way from baggage claim to bus stop.