The Cog Railway is pretty fun, I took one of the steam trains up a couple years ago. It's impressive to say the least. That mountain has some amazing history. There is an also an auto road that you can drive up on the opposite side of the mountain from the Cog Railway. That's fun and scary at the same time because there are places where you don't want to go off the road, people have died. I prefer the train. I plan on hiking Washington this summer too. It's definitely one of the more strenuous hikes in my area. There's one trail going up Huntington ravine that is considered the most challenging and dangerous in the east as far as hiking goes.
You will love the Kancamagus highway, lots of nice views and places to pull over and fish. I do a lot of hiking in that area, the east end of that highway is only about 20 minutes from me. I've never hunted over that way because I have so many good spots near my house but a friend of mine shot a moose in that area.