My specific response (very close-in suburb of very big city).
Not planning to move for now.
PRO: Job market, it's home (grew up near here, family near here, kids settled in school), lots of amenities relatively near here, lots of open-minded, well educated people.
CONS: Taxes (very high), cost of living (very high), traffic, certain aspects of politics (I can deal with both moderate liberals and moderate conservatives, I don't like extremists -- either of the far right or illiberal progressive variety).
I don't know if I will move later. I am content with just running up the score a bit for now, and I also hope to take advantage of the strong job market later with additional job moves. When I tire of that, I may want some change, but by then the kids may be well nestled into schools. Then, the question is whether they want to live here when they grow up (for the job market). If they do, family comes first so I'll probably stay. If they don't, then I may call it quits.
Incidentally, I'm a big believer that Americans often move too much and it would often be better for us to all to just grow deep roots where we are and work to improve what we don't like or just recognize that there are tradeoffs to everything. But COL where I am is really punishingly high (@Buffaloski Boris, people from where I am would consider your state the promised land as far as taxes are concerned), so it's a big sacrifice in my case if the income isn't there to match it.
Interesting. I'm of the opposite belief. I recently read an article about how most Americans still live within XX (50?) miles of their mother. I think that when we only know and see people more or less like us, it makes empathy much more challenging, and makes it more difficult to understand varying viewpoints. If you come from a place where guns are nearly always a tool of violence, it's tough to see and remember that in some places, they are a resource (hunting) or for protecting livestock against predators, as one example. When we only experience one thing, everything else becomes "other" and that helps entrench tribalism. Travel can help with this to some extent, but only minimally so, and especially if you only stay in a hotel and take a taxi to the big ticket tourist sites.
We we live different places, and especially different types of places--WRT politics, religion, racial diversity, socio-economic position, rural/urban/suburban, and traditional values--we gain insights into different people and different value systems. That makes us better able to empathize, and also allows us to shop for the good and bad in each thing when considering what ideal we want to help our current place move toward.
I was thinking about it mostly of the "Bowling Alone" perspective of social isolation and its terrible consequences. I think that sense of isolation increases in transient communities, though that is obviously not the only factor. I propose rootedness as a solution so that folks can rebuild civic institutions and thicken social ties.
I'm also looking at it from the perspective of people moving from one mega-city to another. My suburb is very diverse with a large number of immigrants from all around the globe, so just by living your life here you will meet all types of people. Most of the people who leave here will move to other cities, and so that will be true (though possibly to not quite as great an extent) wherever they move and so I am not sure all that much would change in terms of broadening perspectives.
However, there is a culture clash between here and other parts of the USA and I do find that frustrating (as I alluded to), though that clash in my opinion is not really due to the diversity or immigration but to the values of a certain subset of the (self-styled) elite. Perhaps if those folks had deeper connections with the rest of country, their views on certain matters would be less rigid and we could more effectively communicate across cultural divides (such as the urban-rural divide you are talking about). It's rarely even people's actual views that bother me, it is the literal inability to understand why someone would think differently or to have respect for someone that does even while disagreeing. So my preference would be a community with more ideological diversity, because I think when you need to interact on a day-to-day basis with people who take the opposite sides to issues than you, it can help people consider things differently or remain more open minded. But maybe folks in "swing" jurisdictions can chime in to tell me if I am right or wrong. Anyways, so I get where you are coming from, but from my perspective I haven't seen hopping from one "elite" city to another cause any increase in open-mindedness among the people I am talking about.
I think the phenomenon of "going away for college" or a graduate degree or first job can be useful for the life experience. Maybe we should have a mandatory Ameri-corps type program where people are purposefully assigned to places very different from where they grew up?
After that period of exploration, though, it can be helpful to just pick somewhere and settle and build something, and for those of us fortunate to be from places with great job markets, "where you were born" does actually work pretty well and has some structural advantages. Larger cities have another structural advantage in that way, because you can "find your people" if you want, so to speak, while still only being able to bubble so much given the broader diversity.
I'm also personally a dork, so historically I've learned mostly from books, and so for me that's been the best tool for learning to appreciate different perspectives, not actual talking with people. I could live in the middle of Manhattan or the depths of the sticks, as long as I have my Kindle I'll have access to the whole world. But I recognize that's not a common perspective, or that people can feel isolated if they are in a place where everyone thinks differently than them.