Conservatives want families. That means yards and safe schools. Liberals usually don't, so diversity (i.e. nearby high-crime black neighborhoods) are not a problem, as long as the theater district, museums and all kinds of ethnic restaurants (and other elements of big city life) are a short cab ride away.
Actually, there are a LOT of gentry liberals in the Capitol Hill area of DC now in what used to be horrible neighborhoods. They do have children (tended to by Guatemalan nannies). In some neighborhoods, there are so many gentry liberals that the local public elementary schools are safe and good. So their children attend the public schools. But they’re in private schools by middle school age.