I've been to many of these places and, to be honest, they don't come across as that different. Now, Arizona and NYC, those have always come across very differently to me. Buffalo very different to Washington. But the differences not really any stronger than, say, the difference between Newcastle and Norwich or Cornwall and Liverpool.* But, then again, the difference between Newcastle and New Delhi, say, is vastly greater than any of those.
I wonder if they do come across as that different to people who live there, though. Some differences may not be so obvious if you're not there all the time. For example, I can imagine an American visiting maybe Manchester and Newcastle, and not seeing much of a difference: similar architechture, countryside, whatever - but to people *from* Manchester and Newcastle, they're as different as chalk and cheese?
I think, to some extent, I weary of Americans who have never left the US from making the "the US is more diverse than Europe" claim because, really, it's just an assertion when you've never had any direct experience to draw on. It's always qualitative anyway because it's difficult to measure differences in an objective way but at least, with someone who has travelled widely, you can have an interesting discussion on it.
So do I, to be honest. I also get weary of the 'you couldn't possibly understand how diverse the US is because it's so big and where you live isn't' argument, and the implication that other places couldn't possibly be as diverse as the US is because they're not the same size. Well, yes they can be, and they are - it's just more concentrated in a smaller area, which actually makes the diversity even *more* surprising. I would expect, for example, a population to have different cultures and and dialects and landscapes or whatnot over a distance of 3000 miles; it's perhaps a little less obvious to realise that areas 300 or so miles apart, like say the South West of England and Liverpool, can be so different and just as different as people from Seattle - vs - Alabama (picking examples out of my head).
Also, I know
how big the US is. I'm quite capable of looking at an atlas to determine this, as I'm sure are most other people who don't live there, so I'm always unsure as why we need to have this fact drummed into us quite so much
I'm not at all insinuating that all Americans do this, of course. But it does seem to be an often proclaimed thing.