Boston and Washington ???

Yes I spent 3 days in Boston and it was enough to get most of the things we wanted to do done. Science museum was excellent as was the JFK one. It's a few years since we were there but we bought one of those multi attraction cards - cannot remember the name but it saved us money on the attractions we went to see.
I haven't been to Washington so cannot comment on it.

We spent 10 days in Boston, renting an apartment and loved every minute of it.

http://www.thefreedomtrail.org/

Washington DC is a great city to visit. All of the national museums, including the national zoo are free. You could spend two days doing the various buildings of the Smithsonian Museum on the Mall. The Holocaust Museum is excellent and very moving and you could easily spend a half day there alone. Then there are the memorials like the Lincoln, Jefferson, FDR etc which are must sees. Also very worthwhile is crossing the river and visiting Arlington House which was the home of Robert E. Lee. After the civil war his estate was made into a cemetery. Further down river is George Washington's home Mount Vernon. The city is easy to navigate and there is a metro. Lots of places to eat out, especially in Georgetown and down river a bit in Alexandria VA. You can pack a lot into 3 days. I would avoid taking the little tourist shuttle because it can fill up and people can get caught out waiting to get onto shuttles that turn out to be full. DC can be hot and humid in the summer.

Can't speak for Boston as I was never there, but I say that 3 days is just about right for Washington. The Smithsonian is brilliant; it has several types of museums along the Mall (the long grassy bit that stretches in front of the Capitol where a million people gathered for Obama's Inauguration); for all tastes and totally free. Capitol Hill is really worth a visit and the White House if you can get a tour booked (I didn't). Also, you couild spend hours walking around the monuments, reflecting pool, Vietnam Memorial etc. I was there end of August/ beginning of September; weather is just about right.

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We have been to New York,thats why we were wondering about seeing two places this time.Would anyone suggest somewhere closer to Boston or somewhere closer to Washington because it seems quite a distance between the two cities.

+ 1 on the Smithsonians in DC and on the JFK museum in Boston. Loved Georgetown. Both cities have places nearby that could make a good day trip, eg Baltimore from DC for the Aquarium and port area, Cape Cod (you can get a ferry to Provincetown) from Boston. I also went whale watching from Boston, excellent day out.

You could also take in a baseball game, Fenway Park in Boston is one of the older and more atmospheric grounds, Nationals in DC have a brand new stadium. Don't worry if you don't understand the game, it's a great place for people watching and I always like to see people in another country at play