... I'd list my own personal favorites, but for the most part it would simply be a list of all the trails on that side of the mountain, so there's no point in my doing it.
That's just what I was thinking!
But I was just there, with a freshly (05/27) trimmed-up knee making an inaugural hike up the Valley Way to the (aptly named) Scar Loop..., and was hankering for Adams via King Ravine and down Airline. This is at the top of my local to-do list there, and should be a good candidate for the fit and exposure-tolerant.
I'd also put in a plug for a walk up the Madison Gulf headwall, although it's around the corner from Route 2. It was the shizz
and a bag of chips.
There are a lot of trails I have yet to discover over there, but having just spent a week there (catching fish instead of hiking), I can report that it's compelling!
There's a new BBQ joint in Gorham called Ice Gulch (which I hear is quite a trip on its own!). They had excellent steak and scallops in their market section; didn't dine in.
Speaking of Ice Gulch, try the Randolph Mountain Club guide to local trails: good back-story info ("Appalachia") and ideas, as well as necessaries on the trails themselves.
The fishing was excellent in the mighty Androscoggin, especially below Errol Dam, but also at South Ponds and in the Upper Ammonoosuc in Stark.
The Perch is a tiny patch of breezy heaven: on a good night, no tent needed.
Tell us where you end up!