I would swap out Mystic for New Haven any day! New Haven is a gritty city. Sure, it has Yale, but that's pretty much it.
By late March we are seeing more warm and sunny days. It MIGHT be cold and dreary, but I wouldn't bet on it. Even if it was, Mystic is a beautiful, small New England town. If it's a rainy day you can tour Mystic by car, then head to Essex to tour the Connecticut River Valley via same. Then head to NYC... you're only a couple of hours away. NYC of course has SO much to do you couldn't do it all in a month. Indoors OR out.
I agree that you ought to shave some off Boston. Boston can keep me amused for a couple of days, tops. Providence is pretty much just locals and college kids that time of year. I would give it a day. Based in Newport, if you ever got bored with the city itself (not likely), you could take day trips to Little Compton (Sakonnet Vineyards and Sakonnet Point are good destinations for some gorgeous scenery along the way), or Narragansett (Ocean Ave is your destination here, and don't miss Galilee, a working fishing port) or Jamestown (what Newport would be if it were not tourist central). Newport of so vistor-friendly, compared to Boston. Try to stay within walking distance of Thames St. and there is SO much to do! It's very affordable when you will be in town.
Newport for at least 2 days, then give NYC at LEAST 2 days.