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.
First, go to Data Axle and click on Search under the U.S. Businesses dataset
Then select Advanced Search
First, select the Business Type. To browse different types click on Major Industry Group. Be sure to expand Retail Trade for businesses like grocery stores and Services for social, legal, educational and religious establishments
Then choose the Geography, you can search for establishments by neighborhood (e.g. Delray, Detroit).
After you've selected the establishments you want for your preferred geography, click on Update Count and then View Results