Would like to know how many users search for counties in U.S. in
general and specifically:
Wayne County, MI
Pinellas County, FL
New York County, NY
Orange County, FL

Any info on this topic or the number of searches for major U.S. cities
would be helpful.

You need to define search and search for. Are you asking about Google
and other search engines and did they include a USA geographical name
in the  search request as in 'CV joints Orange county, Florida'
 Mapquest searches? 
 GPS searches?
 Genealogy searches
 Title searches?
 "Hey kids if you see a sign saying now entering Wayne county, yell" 
 All of the above plus hundreds of other possible meanings

Yes. Overlooked. 

Just searches for the County Goverments that I mentioned and the total:

Wayne County Searches for Dec....110,000
Pinellas County Searches for Dec...100

A total: Searches for all counties is 1,000,000. If not too hard to pull together.

Mapquest, Yahoo but Google is main source.

Thank you!