Hi, I live in DC and there is plenty to do here, aside from the White House, and most of the museums, monuments, and things are free! There's a great theater and concert scene as well. The metro is easy and the city's very walkable. Haven't been to Chicago but I have a friend from there who just moved back because she missed it so much! I would definitely recommend some of the national parks out West. It seems pretty do-able to hit the Grand Canyon, Arches National Park, Bryce and Zion national parks all together.
It's also easy and pretty cheap to get from New York to DC on bus or train (passing through Philadelphia - where I'm from - also good for history stuff (Liberty Bell!)) so you may be able to save yourself a flight if you make it a side trip from NY.
Be prepared though, July/August is prime tourist season and many of those places will be crowded. And it is HOT!
Between Chicago and Toronto I'd go for Chicago. But you could drink in Toronto (suffrage is 18 in Canada). If you're flying and going to be in that side of the continent, go for Montreal or Quebec city over either Chicago or Toronto! They blow them both out of the water. You don't have to speak French, but a little French helps.
Also, I'd suggest not planning to sleep on benches and things. Anywhere I've ever found in NA where the benches are sheltered, they close over night, and peace officers/police will generally kick you out of park benches etc in any area you'd actually want/feel comfortable spending the night in.
Thanks for the responses and feedback guys! it's much appreciated! Don't worry shepalie, im sure i'll resist living on benches for a month! I'm thinking of doing a round trip now (due to money and time available because of having to work) either from nyc to DC to Chicago/michigan to montreal to Quebec to boston and back. Or NYC to DC to Toronto to Montreal to Quebec to Boston, and completely miss out all the West coast? What do you guys recommend?
If you are going to the US in the July/August timeframe, keep in mind that this is usually the hottest (and also most humid) time to go. For this reason, I'd probably avoid places way south like Florida or in the exact middle of the country (like Kansas or Texas) and spend more time a little bit farther north (anywhere from Washington, DC to Nashville to New York, Chicago, and Boston)--or in the mountains (think Colorado, Wyoming and Montana) or on the west coast (California, Oregon, and Washington). Also, both Alaska and Hawaii would be beautiful this time of year.
Personally, I think there is a lot to see in Washington DC, but Chicago's okay also. If it were me, I'd try to get to the Rocky Mountains (Colorado or western Wyoming or northern New Mexico) or else the Appalachian Mountains (eastern Tennesee or western Virginia) for some of my trip. This is where you will find the things you don't normally experience back in London.
First off if you are flying about 49 days is a lot of time to see stuff, even a country as big at the US. Having been to both Toronto and Chicago I'd say you can't go wrong either way but my lean is Chicago. Both are beautiful but I was stunned at just how blue and clear Lake Michigan and the Chicago River are, it looked almost like the Caribbean.
I'm a big fan of the west, particularly California, but you have to see NYC and DC. Given your schedule I'd plan on 2 days in each, that will give you the chance to see the basics (Statue of Liberty, White House etc) without breaking the bank. Both cities, NY in particular, are VERY expensive. You could spend a week alone visiting the Smithsonian so I have no idea who would say there is only the White House to see in DC. Keep in mind you always need to be on your toes in any major city but especially in New York. Keep your wallet in your front, not hip, pocket. Stay off the subway late at night, lock your passport in the hotel safe etc. Can't stress this enough.