Google can be quite helpful to find statistics. Use specific words from your research question along with the word "statistics."
For example, you're interested in finding the United States children in poverty by race at county level. Try this example:
Once you get search results, browse them with special attention to the source. If you see too many questionable sources, try limiting to specific site such as .gov by typing site:.gov after your search.
You can also limit to a specific repository such as ICPSR: