The Connecticut River at and up from Pittsburg, NH, is 3+ hours from Henniker, but if I lived in NH, I'd hit it a couple of times per year. The fly - trophy section is like Pennsylvania FFO Trophy Trout streams of the 1970s. Massive amounts of stocked trout, plus some landlocked salmon that are either wild or stocked as fingerlings. There's another fly section, downstream from Second Connecticut Lake to First Connecticut Lake that is all wild brook trout, supposedly with some atlantics running in the fall. If I lived up that way, I'd hit the wild FFO section in the morning and when I had my fill of 5 to 10 inch wild brook trout, I'd go down and fish for the stockers in the "trophy section" and hope to hook into a nice Atlantic.
Two of my cousins and I fished it this past spring. I had wanted to fish that upper Connecticut since I read about it in Field and Stream in the 1970s. It wasn't a disappointment, but it was not the destination spot I had daydreamed about.
Henniker is closer to the lakes region. Smallmouth, pike, and (if you're into it) yellow perch fishing in the big lakes can be very good. I talked to some folks who trailed streamers off downriggers to catch big steelies in deep water (80 feet+), but I never invested in that kind of equipment.
My family vacationed in the lakes district for many summers, and, though I tried, I failed to find any trout fishing in that territory at that time of year. It seemed like the streams and small rivers were devoid of all fish. That territory is mostly dependent on stocked trout, with a some lake runners in the spring and fall (though I never hit that). I was never up there in the spring or autumn, but there is supposedly good winter and springtime fishing for big trout and landlocked salmon running out of the lakes.
A quick note: when I was a kid, I read extensively about the brook trout ponds in New Hampshire, while vacationing up there, I found one and went to fish it in mid summer. Total bust. There were campfire pits every 10 feet along the shore, presumably as a result of springtime meathole fishing. I didn't even see a sunny in the pond, though the scenery was nice and the water was clear and cold. Turns out that brook trout pond experience in the modern era is entirely dependent on stocked fish.
In general, my understanding is landlockeds running out of the lakes (especially into the Connecticut) happens in the fall for the spawn and in the spring when the smelt are on their spawning run.
The one place I never tried, but would invest some time trying if I lived in that area is the Merrimack River, which essentially drains the Lakes Region.
From a trout (and salmon) perspective, if I were to give Maryland and Pennsylvania a B to B+ (the plus for effort), I would give New Hampshire a C- from an angling perspective and an F for effort. Stocking trout in meat holes is not a management strategy. And I realize there's an acid rain problem, but there is absolutely no effort at mitigation such as we have in Pennsylvania and Maryland for coal mine acid.
When I was vacationing there, someone described New Hampshire as "the West Virginia of New England." I'm inclined to agree. Once you leave the tourist areas such as the lakes district, there are vast swaths of land that have been stripped of resources and left to erode. I suspect it's a lot like what Pennsylvania looked like in the late 1800s after it's forests had been mostly clear cut to make railroad ties for the transcontinental railroad.