I first heard about Jane Jacobs' work from Ed Glaeser when he was starting to write his well known JPE paper (1992) testing whether more diverse or more specialized cities grow faster. Glaeser's Dream Team of co-authors found that "Jacobs beat Marshall-Arrow-Romer". More diverse cities grew faster.
Why could diversity foster economic growth? In a dense, diverse city such as New York City, firms could learn from each other and synergies could be realized. In today's sprawling office parks, is there less cross-firm learning? We see Microsoft building and expanding its enormous corporate campus near Seattle. Clearly, learning is going on within this firm but not across nearby firms.
Diverse cities are also more likely to be diversified. Such cities (unlike a Houston) do not put all of their "eggs in one basket". This should mean less volatile local unemployment rates.
Such diverse cities may also enjoy a Richard Florida effect. This author has celebrated the importance of the creative class in making a city thrive and be interesting. It is intuitive that diverse cities (think of San Francisco and NYC) are more likely to score higher on the Richard Florida index.
What I find interesting about Jacobs' work is celebrating the benefits of diversity. Perhaps unfortunately, in my own work --- I have investigated the "costs of diversity" namely that people are less likely to be good civic citizens when other people in their community (broadly defined) do not look like them on income and racial attributes. For a good survey see: http://www.nber.org/papers/w10313
and papers on social capital here: