I know about the weaknesses of the presidency, but what about the strengths?
Being the president of the United States means in some sense being the most powerful person in the world and one has to have enough qualities to merit this position.
The greatest strength of the US presidency is the power that comes with it, that is access to the maximum possible power on this planet, as the commander-in-chief of the most advanced military force. Another big advantage is the access to resources, which the US has aplenty. The president has the right to veto the decisions of the senate and thus can prevent any bill from becoming a law. This provides the much needed "checks and balances" in the government. The president also appoints federal judges, secretaries and top officials of the federal agencies. The president can be impeached by the senate and removed any time during the term; however this has hardly ever happened (for example, Bill Clinton was impeached but not removed from office). That is, they gain the position for at least one term without much fear of losing it. The president also has the right to conduct negotiations, sign treaties and appoint ambassadors on behalf of the nation. And all decisions are enacted in his name (i.e. by his approval).