If you carefully keep your bird records by state, be aware of the location of the state line and use the appropriate eBird hotspots when you submit checklists. The Vermont-New Hampshire state line is in the Connecticut River. 

Bedell Bridge State Park in Haverhill has one of the prime floodplain forests in New Hampshire. Take a left just past the village before you get to NH-25 north of the center of Haverhill.  You can spot birds in the wetlands along the road if you enter slowly. 
From Jim Block

Bedell Bridge State Historic Site is a 38-acre park located along the Connecticut River. The park was the site of a historic two-span-covered bridge, the second longest in the country. The Burrtuss Bridge, which connected New Hampshire to Vermont, was destroyed by wind in 1979 and is no longer there. A Fish and Game boat launch is located within the park.

The TrailFinder website has a description and map of a hike at Bedell Bridge State Historic Site.