If you want great hikes you should head to New Hampshire. Go to Franconia Notch State Park. There are numerous wonderful hikes in the area. Nearby is the Kancamagus Highway which is maybe my favorite drive in New England. This time of year it should be beautiful. There are numerous hikes to waterfalls in that area.

As far as Vermont hiking you might want to go up to The Smugglers notch area. There are a couple of actual hikes around there plus you're close to Stowe and all the things around there. I don't think anyone mentioned Cold Hollow Cider mill which is a fun stop.

For history I really like the Calvin Coolidge Historic Site. They have preserved his entire farm including the room where he was sworn in as president after Warren Harding suddenly died. For some reason I really loved this.

The Calvin Coolidge site is not far from Woodstock which is quintessential New England. And up the road from that is the Quechee Gorge which is a fun but short hike. If you're there, stop at Simon Pearce and watch the glass blowing in the basement of the shop. One of my favorite things to do.

I spend a ton of time in both states. Feel free to reach out if you're looking for more specifics.