The first web server in the United States was hosted at SLAC, the Stanford Linear Accelerator Center. SLAC installed the server on December 12, 1991, after physicist Paul Kunz brought news of the World Wide Web back from CERN.
Kunz worked with librarian Louise Addis and other SLAC staff to adapt the new technology for SPIRES, a major database of high-energy-physics literature. The server made research papers and related information easier for scientists to find across international collaborations.
The original machine was a NeXT computer, the same general type of workstation Tim Berners-Lee had used while developing the Web at CERN. SLAC’s installation is often described as the first web server outside Europe and the first website in North America; institutional histories commonly shorten that to the first U.S. web server.
Stanford University is a related but less precise answer because SLAC was operated by Stanford for the U.S. Department of Energy. MIT and CERN were important in early computing and Web history, but neither hosted this first American server.