Even the most conservative cities in America are barely right of center, as this great chart from the Economist, based on research from Chris Tausanovitch at UCLA and Christopher Warshaw at MIT, shows:
It's no surprise that most big cities are left of center, as the Pew Research Center points out. What's interesting is how liberal even the median big city is. Cincinnati, for example, hangs around the center of big cities' political spectrum, but the Economist's chart shows it's still fairly liberal.
For another look at the liberal and conservative towns and cities each state, check out this map from Business Insider: