Franconia Ridge is easiest going up Falling Waters and down the Bridle Path from Lincoln. This gives you a more gradual descent and an easier path going down. I've done it both ways and enjoy both ways for different reasons.
Tons of great hikes in the 7-10 mile range. Why not Washington? You don't have to go to the summit. Tuckerman Ravine or a loop around Boott Spur and Lion's Head would be grand. Webster Cliff trail is great with a car spot or a bike spot (really cool with a bike spot going down Crawford Notch after the hike). Osceola & East Osceola loop would be great as well (check the status of Greeley Ponds trail though, I heard Irene did some damage).