A car traveling up Mt. Washington is one full of passengers missing out on the area's true beauty. Screw the "This Car Climbed.." bumper stickers, and earn your crappy summit cafeteria meal after spending hours of treacherous foot-ascention to the top. Hike Mt. Washington!
Beautiful pine and hemlock-scented woods await, along with steep ravines, fresh streams, waterfalls, boulder fields, and snow that lasts all the way 'till August. It's a great place for anything from trail running, to hiking, camping, or spring skiing.
However, an advisory: be sure to properly educate and equip yourself before undertaking an adventure here. The ease of accessibility due to the presence of the auto road often softens people's perceptions of the place, resulting in many who lack respect for its true dangers.
Don't underestimate the place. Mt. Washington has been credited with having the "worst weather on earth," also holding the highest wind speed ever recorded (231 mph) up until 2010.
Year after year, it has been home unfortunate deaths, often times due to the foolishness/unpreparedness of those who venture onto it. I have been hiking the mountain since I was young, my father has skied it, and I know someone who died here. While it has trails in varying levels of difficulty, and while I have seen, and been myself, one of the very young kids hiking alongside their parents and grandparents here, this is no place to be messed with.
Enjoy it, but respect it. You won't regret it.