1) Build higher. A lot higher.
2) Massively increase supply.
Put in place a regulation that says all new buildings must be X stories high (20,40,60, whatever.) Along with that, include a regulation that force said buildings to fit in with the neighbhorhood look. UWS and the West Village here in NYC have great examples of extremely tall buildings that are not Jetson's-style eyesores.
Also put in place a regulation that says existing building that can be built higher (while keeping the existing external facade) should be. Where this isn't possible, knock it down and replace it with a building that keeps the old facade.
Change the zoning restrictions and regulations to allow the above, and supply will go up, prices will (eventually) come down, and the neighbhorhood looks will remain similar. Everyone gets some of what they want, and the place stays diverse, vibrant, and does not force local workers to deal with punishing commutes just so they can do their jobs.
The above applies just as much to NYC or any other large city that is holding back this kind of development. As per the UN:
"In 1950, one-third of the world’s people lived in cities. Just 50 years later, this proportion has risen to one-half and will continue to grow to two-thirds, or 6 billion people, by 2050. Cities are now home to half of humankind." Policies need to change to deal with this new reality.