Kathadin is the best hike on the east coast! I highly recommend Cathedral trail up & the Knife Edge! It's the closest thing to west-coast mts we have here. Not sure about June, but early July is black fly season
Also expect lots of fun with anal-retentive Baxter park rangers
There's lots of moose in the park, but not much other wildlife. All in all, Kathadin is a memorable experience. Enjoy!!