My own thoughts: In farmed animal welfare, I think it's possible for EAs to influence state governments to fund research and development on alternative proteins (especially through land-grant universities like Cornell University in New York) and improve regulations on animal agriculture. It may also be possible to change state and local environmental laws to improve wild animal welfare.

Update February 4, 2022: I've become more convinced that most EAs interested in influencing policy should not frame EA causes as foreign policy issues. While this is a useful framing for some organizations (e.g. Center for Security and Emerging Technology, Center for Global Development), it's inherently limiting because it is very difficult for the average citizen to influence foreign policy. It's easier for the average citizen to influence national domestic policy, and easier still for them to influence state and local policy.

Also, I've thought of more EA causes that could be worked on with high leverage at the subnational level:

• Improving institutions: Local and state governments are natural "laboratories of democracy," so they are great venues in which to test novel institutions before scaling them up. I'm particularly excited about experimental institutions that could improve democracy along these dimensions. For example, many municipalities have adopted alternative voting systems, such as ranked-choice voting and approval voting. I'd also like to see more experiments with novel approaches to deliberative democracy, such as quadratic voting and whatever Polis is.
• Biosecurity: U.S. state and local governments have enacted various responses to the COVID-19 pandemic, with varying results. We could lobby for policies to help state and local governments prepare for the next pandemic.
• Climate change is another policy area where state and local governments can take the lead (and have done so).
• AI regulation: there is some precedent for state and local governments regulating information technology, such as the California Consumer Privacy Act and San Francisco's facial recognition ban. Likewise, states could be laboratories for regulations designed to mitigate the worst risks from AI and other emerging technologies.
• Mental health and extreme poverty could be worked on at the state and local levels.

I started to write a more thorough response to this but realized I was essentially copying Rethink Priorities' post on Ballot Initiatives, which covers a lot of EA causes with high leverage at the local/state level.

Two popular EA causes that I think are missing:

• Climate change interventions
• UBI (difficult, but not impossible to enact at the state level in the US because states can't deficit spend. See Alaska as an example)

I agree with evelynciara that animal welfare in agriculture is highly relevant to EA and that most progress toward animal welfare laws are being made at the state and local level. I would add that progress towards national and global goals often starts at the local level--more states adopt a particular law (e.g. increased welfare standards in agriculture), and that sets an example for others to start a more national conversation. 

Other things that come to mind are scalable improvements in institutional and governmental decision making such as adopting approval voting. These are  important for similar reasons to animal welfare laws--they set an example and set the stage for a national conversation.

Local governments also fund universities and other research programs that might be high impact and in principal they could fund much more and much more effectively. They have jurisdiction over housing, zoning, and transport which have enormous environmental and economic impact. They have at least partial jurisdiction on mental health programs, policing, criminal justice, vehicle and pedestrian safety, lead abatement, and charitable grants.

With that said, no one can make much of dent in nuclear weapons policies by showing up to their local city council meeting, so there is plenty of work to be done on the federal level as well and where any individual should focus probably depends on their personal situation, skills, interests, etc.