Tons. Arguably even most of governance is not done at the federal level. This is why every city and state has its own governance and pass their own laws and ordinances. I'll enumerate a small and by no means exhaustive list:
Things like garbage collection, parking tickets, zoning, tourism boards, etc are all almost exclusively handled at the municipal level. Its possible that the municipal governments may receive aid and funding from the federal level that may come with some restrictions, but the final decisions rest solely in the hands of the municipality.
Police departments will be funded by the local government, but the laws they enforce will mainly be state laws. Take for example murder. Unless you cross state lines that will be handled entirely in state.
This actually is handled by the states. They have full discretion over the drinking age. Now they have all decided to make the drinking age 21 because they don't want to lose 10% of their highway funding, but they are not forced to do so. Any state can lower their drinking age tomorrow. In fact, even after the Drinking Age Act was passed some states held their drinking age at a lower number (Louisiana held out at effectively 18 until 1995, 11 years after the act passed).
States can define their own constitutions that really don't need to look anything like the US constitution (with one exception being that they must be a republic). The federal government does not control what goes into a state constitution.