Hiking is fun and so is cycling. Generally, though, the hike a bike is not something the people seek out. It's good for character building, but you try to avoid routes where you spend an hour carrying your bike your shoulder. I did this once and was proud to say that I did, but I'm not jumping at the chance to do it again. Hiking is best done without a vestigial bicycle.
What I do recommend is riding to a hike and then locking up your bike. You get to spend maximum time outside and it discourages going too fast: you don't want to ride too hard so that you have energy to hike and you don't want to hike too far so that you can ride home. I did this yesterday wherein I rode over to Ragged Mountain, met some friends and went for a hike and then rode home. Originally, I was going to get a ride home, but apparently everyone thought I was super tough and didn't bring a bike rack. This probably doesn't work if you're planning to go hike Mount Adams or something starting from Connecticut in a day. It does work, though, if you want to go to Ragged Mountain or Heublein Tower or something more low key.
It's sort of the same principle as riding your bike to go fishing.
Ragged mountain is mostly not all that great for mountain biking. Would anyone want to ride on this? There are a couple of interesting sections of singletrack off in the unpopular part of the Reserve over by the powerlines.
I was lying on this rock for a half hour yesterday looking at the trees and contemplating my trivial existence.