There are a ton of places to find data related to public policy and administration (as well as data on pretty much any topic you want) online:
Data is Plural newsletter: Jeremy Singer-Vine sends a weekly newsletter of the most interesting public datasets he’s found. You should subscribe to it. He also has an archive of all the datasets he’s highlighted.
Google Dataset Search: Google indexes thousands of public datasets; search for them here.
Kaggle: Kaggle hosts machine learning competitions where people compete to create the fastest, most efficient, most predictive algorithms. A byproduct of these competitions is a host of fascinating datasets that are generally free and open to the public. See, for example, the European Soccer Database, the Salem Witchcraft Dataset or results from an Oreo flavors taste test.
360Giving: Dozens of British foundations follow a standard file format for sharing grant data and have made that data available online.
US City Open Data Census: More than 100 US cities have committed to sharing dozens of types of data, including data about crime, budgets, campaign finance, lobbying, transit, and zoning. This site from the Sunlight Foundation and Code for America collects this data and rates cities by how well they’re doing.
Political science and economics datasets: There’s a wealth of data available for political science- and economics-related topics:
- François Briatte’s extensive curated lists: Includes data from/about intergovernmental organizations (IGOs), nongovernmental organizations (NGOs), public opinion surveys, parliaments and legislatures, wars, human rights, elections, and municipalities.
- Thomas Leeper’s list of political science datasets: Good short list of useful datasets, divided by type of data (country-level data, survey data, social media data, event data, text data, etc.).
- Erik Gahner’s list of political science datasets: Huge list of useful datasets, divided by topic (governance, elections, policy, political elites, etc.)