In reply to RB1:
There is a ton of hiking on Vancouver Island. There are great hikes around Squamish too of course but there's something special about both the coastal hikes and mountain ridges on the Island.
The suggestion of the North Coast Trail is very good but that's a week long expedition requiring some expensive logistics and a lot of driving. For a coastal hike more in your time frame I'd suggest heading out to Tofino and taking the water taxi to Flores Island and hiking the Wild Side Trail. Its one of the quickest, least expensive ways to experience the 'outside' coast, proper wilderness, big trees and First Nations' territory. You won't believe the beaches there.
There are great shorter hikes all over but some of the outstanding ones can be found on the smaller islands off Vancouver Island. From Squamish you're better off coming across on the ferry to Nanaimo and going west (Tofino) and north from there, (at least as far as Campbell River area). Quadra Island is a gem with miles of great day hikes, sport climbing, single-track mountain biking and world-class sea kayaking all around it. Gorgeous place!
For the 2-3 day hikes head from Campbell River up to Strathcona Park. Look at the Elk River Trail, Bedwell Lakes Trail or Flower Ridge. Each of these can offer fantastic experiences in 2-3 days. Hiking on gentle meadows with views of alpine peaks all around. Lots of options for longer and shorter hikes.
Hope you have a great trip.