Often, the place to find and store data are the very same. Researchers will place the data they collect into general or disciplinary repositories. While other researchers can search those repositories for data and datasets on their topic. Some repositories are costly while others are considered "open" and offer data freely for anyone to download.
Although both terms are commonly used synonymously, they are, in fact, very different. Before you start searching for either, think about which one best applies to your needs.
The National Library of Medicine has a great resource full of other data-related definitions.
A data repository is a storage space for researchers to deposit data sets associated with their research. And if you’re an author seeking to comply with a journal or funder data sharing policy, you’ll need to identify a suitable repository for your data.
An open access data repository openly stores data in a way that allows immediate user access to anyone. There are no limitations to the repository access.
You can search for specific file types in Google, for example CSV files for datasets. By typing into Google filetype:csv in the search bar you are "telling" Google to only search for things that have that specific file type. For example: (poverty AND ohio) filetype:xls will result in XLS (Excel) files mentioning Poverty in Ohio.
Limit search results by web domain by typing into Google: site:.gov (YOUR TOPIC HERE) . This will limit datasets, files, etc. from specific websites. You could even do .org for professional organizations.