I recommend parking at Race Brook Falls trailhead in Sheffield, MA, a few miles north of the CT/MA line on Rt. 41. It's a 2 mile hike from the A.T. along Race Brook, between Mts. Race and Everett, with a very nice stretch of waterfalls in the second mile. Once you get to the brook crossing below the upper big waterfall (about 75 feet high), take the branch of the trail which goes along the south bank of the brook. You'll see 5 waterfalls in the space of about a quarter mile of trail. Wonderful little trail.
The proper CT/NY border is on Hoyt Road just south of the Rt. 55 parking area. You can park at Rt. 55, as coach lou said, or at Hoyt Road. The 55 parking area is more spacious.