You'll find numerous institutions of higher education in the area, ranging from large public universities to smaller private colleges. To get a precise number, you'd need to:
1. Define "University": Are you including colleges, community colleges, and specialized institutions?
2. Define "Piedmont Region": The borders aren't strictly defined. You'd need to use a specific geographic definition or map.
To find the answer, you could try searching online for a list of colleges and universities in specific Piedmont cities (like Charlotte, Greensboro, Winston-Salem, etc.) and then combining those lists, carefully considering your definitions from steps 1 and 2 above.