We take the MurphDog up Bear Mtn (there are 2 or 3 different trail options) all the time - he loves it.
Plus, he gets to swim in Hessian Pond at the bottom.
He did Anthony's Nose when he was just a wee pup, it was a bit too much for him then, and my wife had to carry him back down.
It's no problem now.
He doesn't have a pack (lazy mutt - or is that smart doggie?
), so he relies on us to carry his snacks, water, leash, etc.
He also hikes w/ us in Fahnestock, on the AT, up Breakneck Ridge, Sugarloaf, Castle Rock, Taurus, Mt Beacon, Schunemunk, wherever.
(He comes climbing on occassion too, but he's a very good dog, so leaving him at the base hasn't been an issue thusfar. - don't take my word for it, crackers, phil, phlan, etc. can vouch for him
Can't help w/ the pack question, but other than severe scrambling routes (like Giant's Workshop - that's too much for any dog), you should be able to take your dog hiking anywhere that you go.
(we even took him winter camping once, he did fine.)