Mt. Washington (6,288 ft.) the pinnacle of the Presidential Range. Mt. Washington is located in the White Mountain National Forest. A very popular spot for outdoor enthusiasts, hikers, ice climbers, rock climbers, skiers, etc. You can hike the mountain, Drive up it, and I believe you can still ride a train up as well.
I have hiked in from Pinkham Notch, up Huntington Ravine, across the Great Gulf, over the Six Husbands trial, up Jefferson, and down to a car parked on the Jefferson Notch Rd. a nice day hike, over 12,000 ft. elevation gain.