Yes, there's some pretty good hiking in North East. One place that jumps out at me right away is Taconic State Park in this town, which makes up a lot of the little panhandle of Dutchess County and carries on up into Columbia County, and the parkland even bleeds into Massachusetts. Around here, there is definitely hiking through the mountains which make up the area (for example, the highest point in Connecticut is right at the state border in this park); there are many miles of trails running through here.
Without having been there myself, I've heard the hikes are quite scenic and beautiful.
