Oh Stefano! You're going to three of my favourite American cities, Washington, Philadelphia and New York. (I've never been to Boston...)
Philadelphia - there are numerous hotels downtown, however I would highly recommend you choose a boutique place in Society Hill which is a gorgeous suburb within walking distance to everything (on a good day) - or short taxi drive.
Dont forget to have a phillie cheese steak sandwich. There is a diner on every corner that serves these (not literally) - but best place is at www.phillycheesesteak.com/
I also really loved going to Chickie and Petes in South Phillie before a game, they have a special taxi "Crab" for patrons to the game after indulging in beer and fries. www.chickiesandpetes.com/
I was taken to Cuba Libre for dinner one night www.cubalibrerestaurant.com/ as an introduction to Philadelphia - this has become one of my all time favourite restaurants!
I used to just wander around and stop by delis and cafe's which were easy to find a place to eat/drink.
Washington - there are certain parts of Washington you just don't go near, but staying close to the central business district, there are some great little family spots within walking distance to the museums, white house etc. The Raddison near Stanton is quite nice and affordable for family rooms.
Finding a decent restaurant was a little bit of a chore in Washington, sadly one day I had to rely on Starbucks for my daily sustenance! (Sunday, not a lot open!)
New York - My all time favourite. Standard Hotel for dinner and cocktails if your budget will allow - at dusk! Apart from that, the touristy places like Bubba Gumps, any little local restaurant in Soho, the Boathouse or my best meal there was a picnic I made for myself and ate in Central Park.
Being Australian, I wasn't quite used to the amount of melted cheese on everything, or the large servings. My budget of $50per day for food was more than ample and in fact some days I went without breakfast or dinner because lunch was huge! almost 7 years ago