"It was built around 1900, and lots of people visit just for the atmosphere. If we could clone this neighborhood and built it elsewhere, it would be a good thing. But we don't seem to be able to build neighborhoods in this style anymore."

A few things ...

First, I think there are some decent examples of what you're looking for ... Minneapolis comes to mind, as you stand in the center of Loring Park, which has a fair amount of new, high density surrounding it. Denver, certainly, as you walk to the North end of 16th st. and cross over that weird bridge ... lots of brand new high density office and residential all arranged and balanced in a very pleasing way.

Anyway ...

One of the reasons people like your neighborhood (I'm guessing) is that the built environment is much more substantial (and honest in use of materials). But we can't afford that anymore. 10x10 timbers and big stones and bricks are (relatively) tremendously expensive.

We can only afford stick built 2x4 construction covered with engineered faux-stone facade, and deep down, people know that's crap. That's why they like a neighborhood like yours.