Classifying USA medical facilities as rural or urban from address or zip code R

I have a list of thousands of USA medical provider locations (street addresses, zip code and state details) and I need to classify each one as either urban or rural. I have no lat long details and my company will not allow me to use my own personal google account to pass this info to Google Maps API to geocode these addresses.

I am using the R programming language but unfortunately have very limited GIS experience (have used MapInfo previously) so if anyone has suggestion how I can classify each location I would be grateful for any info.