Points of historical or cultural interest between New York and Boston

If you decide to drive the coastal route (I-95) Mystic Seaport is amazing. If you decide to travel I-91 to I-84, The Mark Twain House & Museum in Hartford is phenomenal. You can then stop at Old Sturbridge Village (Massachusetts) just over the CT/MA line. It's a large, faithful recreation of a late 18th/early 19th century rural New England village/farm.

In Plymouth there is Plymouth Rock of course - a little anti climatic, but a must if you are in the area - nice view of the ocean.  There's a place called Plimoth Plantation - that would be great for the kids.  It shows how life was back when the pilgrims landed.  There's a replica of the ship used to cross the Atlantic it is a good eye opener.

Cape Cod could be far to go for a day depending on where you go, it's pretty spread out.  

In Boston - a must is the Freedom Trail.  Do a tour and or audio guide, take your time.  Best history lesson every.  I lived in the area for 40 years before I went with a visitor.  Should have done it years before - it would have helped me with history :).

I have to disagree with Alexa regarding Providence. I lived there for 5 years and in my opinion is quite steep in New England culture plus over the years it has experienced somewhat of a renaissance and is a great place to spend a ½ day or day. Some of the highlights are RISD, museum of art & design, John Brown House Museum and the Governor Henry Lippit House Museum. The East Side (where Brown University is located) is rife with 18th and 19th century architecture and is small enough to walk around and see everything. For more information on what is there I would check out www.goprovidence.com.

Providence does not have much of that rich New England culture . Although if you go on a Saturday you can go up to the Hope St Farmers Market which is a big thing there. Plymouth (Massachusetts) is historically rich. Going to Newport in the summer is the way to go, it is a beautiful place.