I think the logic stated in the OP in support of the Electoral College is flawed. Regardless of where a person resides (urban, rural, big state, small state), in a popular vote all votes equally count. The idea that only several cities would count is flat out wrong. All votes would be tallied with equal weight, so every voice in the nation would count with equal weight.
If the intent is to have a democratically elected president, then a pure popular vote makes the most sense. Democracy is government by and for the people. Democracy is NOT by and for the states, which is what the EC warps the democratic process into to a very significant extent. That is characteristic of a republican form of government instead, and a republic is just an elite-controlled state or nation. There's a long history behind the system we have today, going all the way back to the original constitution which actually placed the election of the president and vice president solely in the hands of an (mostly wealthy white male elite) elected congress and the then-state-appointed (not elected) senators (the United States was not founded as a democracy, but as a republic with very limited democratic features, contrary to popular belief; we've instead been
approaching a democratic ideal throughout US history). The EC has continued to its present form as a way to cater to some old concerns which no longer really apply.
Or
should no longer apply... I think the inspiration behind these common arguments in defense of the EC is the way in which presidential candidates conduct their campaigns. Candidates travel throughout key areas (not all areas, as another poster rightly mentioned already) making speeches to impress the people local to each area. If the EC were abolished in favor of a pure popular vote, this would probably shift this present method of campaigning to indeed focus on several key cities. But this problem can be resolved with serious campaign finance reform. At present, candidates are funded by a combination of personal wealth (an implicit requirement to be both rich and biased towards your personal financial interests), corporate contributions (ensuring candidates are beholden to their corporate sponsors rather than the people, thus subverting democracy), and individual contributions (also problematic as it gives greater voice to those with more money than others). This system enables money to be transferred into political clout, which is a subversion or corruption of democracy. But if we criminalized all private campaign contributions, and eliminated the entire model of candidate campaigning throughout the nation, and instead simply set aside a small public fund for the candidates to have a series of publicly televised debates as well as maintain informative websites, this would not only criminalize a ginormous source of our governmental corruption but would eliminate the need for the EC. The presidency is a national governmental position anyway: as another poster already mentioned, strictly local interests would best be dealt with by local government officials. Also, on a related but perhaps a side note, I am in favor of abolishing political parties: too many people vote for their team like they're playing football, while the parties themselves are a subversion of democracy via their control over the candidate pool. Eliminating the parties would force candidates to run more on their individual ideas, rather than by how well they conform to the dictates of their party.
I could go on, but I'll stop myself here.