We travel with MH & toad from Maine to Lancaster County, PA several times a year. Plan on crossing the Hudson at Newburgh, on I-84. Less traffic and the toll is cheaper than anything that I ever paid on the Tappan Zee. The other major thing you need to know is that the price of gas/diesel in NY and CT is the highest in the northeast. Fuel up in NJ, and you should be able to make it to NH/southern Maine. Once you're on I-84, stay on it to the Mass Turnpike in Sturbridge. Go east one exit, and take I-290 to I-495 to I-95. Traffic in Hartford, CT. can be slow going during rush hour, but is easily doable.
Hope this helps. Enjoy your trip.