Congrats on the new boat. Sounds like fun. I don't think your itinerary is too ambitious, assuming the weather and the boat cooperate. But that said, it also depends on how much you are willing to be at sea, and how much you are willing to motor if the wind does not cooperate. For instance, the trip from BI to Cuttyhunk is about 25 miles, plus or minus. If you could sail the rumline at 5 knots, then that's a 5-hour trip, obviously. But, if the wind is light, or out of the east so that you must beat into it, you will be much slower, and that same trip could take you 7 or 8 hours (not to mention if you have a foul current). Same trip, you are willing to put the pedal down and motor or motor sail if the wind is not right, you probably can maintain 6+ knots and get there in 4 hours or so. So how far you get in many ways is up to you. When we cruise this area we try to be flexible, and either recognize we'll need to motor some of the time, or we alter our itinerary, either to stay put an extra day until the wind is right, or sail somewhere to a different place than planned.
In terms of the places you identify, they all are favorites of mine. But you made a comment that makes me wonder about something. What does your son like to do? If he likes the beach, that would mean going one way. If he likes nightlife, that would mean another, and so forth. With that, I'll give you my views on the places you identified.
Block Island. It sort of has it all. There is a great beach, with fun surf. There is a cool downtown area with restaurants and such. And there are a number of fun bars for nightlife. In terms of where to stay, I would urge you to consider staying on a mooring and use the water taxi. The moorings are so much more pleasant than the docks, but that's just a personal opinion. If you go dockside, I would strongly recommend Block Island Boat Basin over Champlain's. Champlain's is a fun place to be, but sometimes not a fun place to dock. If you get an inside slip so that you are by yourself, then it's fine (though the docks are not floating). But, and it's a huge but, there are several spots there where they raft boats, so you either need to climb over other boats, or you have strangers walking all over yours. Usually it's a little of both. Now, Memorial Day Weekend is one of the two or three most crowded weekends on that island. It is going to be a zoo no matter where you go (unless the economy hits even harder than expected, but even then, I suspect that the main weekends still will be crowded, and the intervening ones might be hit harder). If you are going to be at BI for that weekend, I strongly urge you to get a reservation at the Boat Basin, or possibly Payne's Dock, and do it soon. I would be surprised to learn that there are openings. And the moorings are first-come-first-serve, and getting there Saturday for Memorial Day Weekend likely will mean you don't get a mooring.
Cuttyhunk. A very pretty place with very little to do if you are not enamored with walking the beach and reading a good book. From what you've written, it might not be a highlight for your son. As you say, however, it is a great stopping point between Martha's Vineyard and BI/Newport.
Martha's Vineyard. Either of Vinyard Haven or Edgartown are great. Plenty of things to do and places to stay. I prefer Edgartown, but that's just my preference. I think the opportunities to go dockside are better at Edgartown too, but I'm not 100% certain. Note that dockside anywhere on MV will not be cheap.
Newport. Another "has it all" spot. Moorings, docks, anchorage, restaurants, bars, shopping. If you guys can't have fun in Newport, then you just can't have fun.
Joking aside, I don't know too many sailors that don't like Newport. Even if you think it's too "built up," there are many places to go and get away from it all.
Point Judith. They don't call it the Harbor of Refuge for nothing. Not a hot spot, but a place to stop on the way to somewhere else (no offense to all you Point Judith yachties).
If you could get a spot in BI, I probably would go from Noank to BI, to Vineyard Haven (long day), to Cuttyhunk (by that point one day on the boat with some quiet might not be so bad), to Newport, to Noank. If you can't get a reservation in BI and intent on leaving on the Saturday of Memorial Day Weekend, then I would consider flipping BI and Newport (that is, go from Noank to Newport, to the Vineyard, to Cuttyhunk, to BI, to Noank). Mind your currents (get Eldridge), on travel days leave in the morning when the wind is light so you get your sea legs in relative calm each day you move, and go have a blast!