Data Axle (formerly ReferenceUSA) can provide counts of businesses (like daycare centers) in a particular city, zip code, census tract or a radius of your choice. It has counts for other establishments related to health care, legal services, educational institutions and religious organizations. More information on the business dataset can be found here.
Then select "Custom Search"
Then start choose the Geography, you can search for establishments by neighborhood (e.g. Delray, Detroit).
Then choose the Business Type. Be sure to expand Retail Trade for businesses like grocery stores and Services for social, legal, educational and religious establishments
After you've selected establishments click on "Update Count" and then "View Results"