Venture into the Pemi my friend, either a "Pemi Loop" or a traverse from Lincoln Woods to either Zealand or Crawford Notch.
There's a number of places to stay around the wilderness including Liberty Springs, Guyot Shelter, Garfield Shelter, Ethan Pond, Galehead hut, Zealand Falls hut, and other good backcountry spots.
To steer clear of the crowds you might want to avoid the huts. Also theres good camping below Bondcliff. Buy the White Mountain Guide if you havent already.
Whatever you do, I'd advise to include the 3 Bond peaks into your itinerary to satisfy your scenery criteria, as I'm sure others would agree.
Bang for your buck, I'd agree with Artex and say go for the Pemi Loop, the potential crowds on Franconia Ridge will be a small price to pay for the rest of hike.
Enjoy!