How much could a tourist learn? Nothing at all except what those cities are like; and that's if you really explore them in depth. Even then, two weeks wouldn't be enough time to really understand those cities' culture, much less american culture. That's an honest answer. Even leaving those cities and exploring the states that those cities are in, there is a huge difference in the people and culture throughout those states. The same is true for most states.
The US is HUGE and has roughly 320 million people living all over. The only way to explain it to where it might make sense is to consider the states being 50 distinct countries, that even have their own laws. Compare it to all of Europe. You could pick 4 cities to go to out of all of Europe, but would that be representative of all of France, Germany, the UK, and every other country in Europe? No. The same is true in the US.
That's about the best example I can give you.
I do believe you'll enjoy yourself though, and there are a lot of things to do. I really love Boston, DC, and NY, and would definitely recommend them for a vacation.
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