Skip the kayaks and use a canoe. You'll be happy that you did. For a nice two to three day trip get yourself a permit for either Homer or Brule entry points. Chance are if on a weekend, the Brule will be full, but often, you can just walk into the ranger station and get a permit for Homer. If you start on Brule, grab a campsite early the first day on one of the islands just out from the entry point. Paddle around on Brule. If it's windy, expect some real 2 footers ("much bigger than what most people call two foot") up to shoulder high. The next day head to Jock Mock Bay, portage an easy portage into Juno and Vern and then snag a site there. If you're motivated, head off into Pipe for your third night or head back to Brule. If you camp on Pipe the third night, exit on Homer and walk back to your car (it's nice to stash a bike at Homer). Picture below looking at an area hit by a forest fire years ago. It's on the portage from Juno to Vern.

You have many many other options. The paddle to Rose is amazing. Something around Sawbill. Or hit the tip of the arrowhead for some long narrow lakes.