If your dog is active it shouldn't have any trouble...Cascade and Porter are quite easy terrain. From what I've done and what I can remember, Algonquin, Phelps, Giant from Rt. 73, and Dial/Nippletop would all be dog friendly. Make sure you read the trail desriptions, the more detailed the better as you may want to avoid any trails involving scrambling. My first trip to the High Peaks I watched a dog try to climb the last part of Iroquois and cut its feet all to hell.