If the best we can come up with is democracy (and that will fail if the voters become too stupid, fearful, or welfare oriented), then we should at least do it right.
The electoral college might have made sense for a loose amalgamation of states, but that hasn't been the case since the civil war. If we're going to be stuck with a strong central government, then lets at least let the people vote directly for the man who's going to run things.
Letting congress pick the president if none of the candidates gets a majority is downright dangerous and frightening in its implications.
Having an entrenched 2 party system guarantees corruption and vested interests. It is almost impossible for a 3rd political party to win a presidential election, and if one does, then one of the older parties will fold up and we'll be back to 2 parties again. What you need is newer and older groups competing on an equal basis. And you need to have the established parties worrying about new upstarts to keep them efficient and reasonably honest.
Having only 2 viable parties means that you are usually choosing between the lesser of two evils instead of voting for somebody you want and makes it possible for elections to be manipulated on a "hate" vote instead of on merit.
What we need is a "Second Chance" voting system. You vote for the person you want, and specify a second choice which replaces your vote if your candidate is not one of the top two in the first round of counting. This lets you vote your desire first and then fall back to a practical, but undesirable, choice. At a minimum, this scares the established parties and causes them to shift quickly in the direction of reform groups that pick up high percentages in the first round. And in the best case, it brings new parties in quickly and overturns the back room king makers.
This kind of voting system is often used in things like picking the best novel or film to avoid the problem of people voting for what they think will have a good chance instead of voting for what they really think is best. Because there are so many contenders, they usually use 3 to 5 choices and multiple elimination rounds. We might want that eventually, but for now its hard enough to explain the idea of two choices.