I would recommend Barkley for this time of year. Like hambone9 said, for whatever reason the migrating fish stay on the outside of nootka early in the season whereas in Barkley they seem to venture deep into the sound in June most seasons. You can fish a lot of protected waters near Bamfield and the Cree / Meares / Swale side of the broken group. Diplock and Fleming usually offer some protection from the normal wind patterns. The fishing can be fantastic in June.
If confidence is low fishing these spots, try fishing a 3.5'' spoon in green/nickle, copcar, or green glow about 5 - 6' behind a green hotspot flasher. Springs at this time of year will usually be between 70 and 120ft in Barkley Sound at any of the hot spots. Find the bait balls and you will find the fish.
IMO the best way to get to Bamfield is by boat, launching in port alberni and running down the canal. You need a good seaworthy boat and the right weather to do it though! The road to Bamfield can be pretty rough on the boat and trailer most of the time.
Have fun with your kids!
Edited: June 17, 2014 12:39PM