New Haven is not a wonderful City but you will probably enjoy the museums etc associated with Yale University.

If you are really intent on walking only (not renting a car), that does limit where you can go.

How about Providence, RI. Amtrak goes here, and it's an interesting town that's navigable without a car.

Or you could combine Providence with Newport.

Wow! That was fast!

Go get a drink of water and already three responses!

Yes, I was thinking of New Haven but was wondering if there was enough for two days - been there a very long time ago and have no memories at all. Vague recollection is that there were a number of museums. Didn't the Melk Abbey in Austria rebuild itself after WWII from the proceeds of the sale of its Gutenberg Bible to Yale? Or was it to Harvard?

Providence sounds like a possibility - does it have as many museums as New Haven?

Decisions! Decisions! already!

Fra - been to Newport several times and it is a destination in itself. Unbelievable mansions!

Have you considered Hartford? I'm pretty sure Megabus has a route there from NYC. Their Wadsworth Atheneum has a nice collection. The DT area is fairly compact. You can also tour the State Capitol bldg and the Old State House.

The Mark Twain House is located a few miles outside of Hartford. It can be reached by public transport. http://www.marktwainhouse.org/visitor/hours_directions.php
However, the immediate neighborhood surrounding the MT House is a bit gruffy; but I suspect it should be safe during day time hours.

Here's a day trip report I wrote a few years ago (I had a car)
http://www.fodors.com/community/united-states/yks-day-trip-report-hartford-ct-for-9-hours.cfm

Otherwise, Providence is a good idea too. The RISD museum is very nice and quite eclectic.

Another possibility is Winterthur in Wilmington, Delaware. It's probably more complicated to get there w/o a car, but it's possible. http://www.winterthur.org/?p=371 I have never been but it's high on my list. CentralParkGirl wrote a nice TR on Winterthur a few years ago.

My vote is for Mystic, CT. 2.7 to 3 hours by Amtrak. The Mystic Seaport museum is only 1 mile from the Amtrak station.
http://www.mysticseaport.org/index.cfm?fuseaction=home.viewpage&page_id=A77B56D7-A9EC-6562-A6CDF7AD4B083BC3

Northeast Regionals leave NYP at 7 & 10AM and 1PM.

yk: No, never considered Hartford. It's always meant "insurance" to me.

I will go and research Hartford and Winterthur as well.

Thank you all very much for your suggestions! I've got plenty to work with for this year!

Tom: Thanks for the suggestion of Mystic, but been there already. Agree that it's a good destination for a couple of days.