The Upper Squamish is all about canyons - big and incredibly scenic canyons. You get the same sort of canyons as found on Dipper Creek without having to run any big waterfalls. Truth be told the Upper Squamish is of little interest as a good kayaking run because of difficult access to paddle class III-IV or unrunnable whitewater. Despite this, it is worth doing to pass through the gorges. Do it at low water - it will quickly fill up and get very scary with any amount of water and to the best of our knowledge it hasn't been run at anything but low water in the shoulder seasons.
Access is along the Squamish main logging road. Head out of Squamish and up the Squamish Valley Road - pass the Ashlu and keep going. It's a bumpy ride that takes almost an hour. At the Elaho/Squamish confluence take the main river left road up the Squamish. At the first major spur head down to your left to a bridge over the river where you can put in. Put in options also exist upstream. The obvious way to take out is to paddle all the way down to where the road is right next to the river, but a large portage in the third or fourth canyon makes most groups bail early and hike up to the road.
Flows on the Upper Squamish should be appropriate when everything is low. It might be possible with a little bit of water but it's almost certain to be unrunnable when there is any semblance of summer flow in the river. There should be a loose correlation with the Elaho gauge - 30 cms is a good flow to try. If you do run this at higher levels scout everything before dropping in. Getting trapped in one of the canyons is an issue that must be considered - a badly placed piece of wood here could cause a major problem.
If you start at the bridge, bushwhack down the river left gully to get to the water. You'll boat some wide open stuff and shortly come to the first canyon - the entrance is unrunnable. What follows are a series of canyons with nice rapids and a wood situation that shifts from year to year. There have been seasons where some sections are completely unrunnable due to wood placement. Perhaps the most impressive part of this run is the canyon below the Dipper Creek confluence, where the water level doubles. In this lower section, you'll eventually reach an obviously unrunnable pile of sieves, which is where most groups hike out to the road (it's a slog, but not a terrible one).
The Upper Squamish is fully worth the trip, but maybe just once every other year. There's still a fairly large chunk of river that hasn't been explored above the bridge where you start. If you're doing it as the paddle out from Dipper Creek, the canyons below Dipper are some of the nicest on the Squamish.