Federalism was, of course, conceived as a way to balance state interests with the collective need for a stronger central government. The biggest advantage of federalism, at least in theory, is that it provides the benefits of a strong central government (especially unity on foreign policy and more or less uniform commerce regulation) without impinging on local needs at the state level.
It was also widely believed in the eighteenth century that no republic could encompass such a large area as the United States, so federalism also had the added advantage of placing some responsibilities in the hands of state governments.
Finally, another major benefit of federalism is that it institutionalizes the diversity of the United States by allowing states to make their own laws within the framework of the US Constitution and federal law. Laws that might work in a east coast urban state (hunting laws, for example) might not be as relevant in the West. So federalism allows for diversity of interests.