The trend to bigger government and bigger politics is clear. With that we get ever more discussions of inequality. Current tax reform discussions gravitate to who will get (or lose) what. Growth (a bigger pie instead of allocating pie slices) gets second place.
In a world of Death of Distance or The World is Flat, cities would have a minor part in the increasing inequality discussion. But neither of these have come to pass. The highly skilled are paying big bucks to be near similar people. They surely engage in electronic interaction but feel strongly about complementing these with the possibility of personal interactions. Hence the value of proximity (even if not cheek-by-jowl) -- and very high rents in San Francisco (and environs), Los Angeles, New York, etc.
That's the demand side. The supply size and the role of regulation have been commented on in various places. For one-stop shopping (reading) http://www.newgeography.com/ has assembled much of the relevant research. See also Enrico Morretti's The New Geography of Jobs.
Many people now have the wherewithal to bid high for selected locations and, in the process, greatly enrich property owners in these places. We get housing wealth inequality compounding the inequality trend.
What can be done? Make it less difficult to build and develop. A minor irony involves the fact that those who fret most about housing "affordability" problems like the tough regulations the most. Their answer is more "affordable" housing provided via various programs. But programs make it worse -- and will never match what market forces could accomplish -- if allowed to.