Generally, records held at the State Dept. are recent (e.g. last 25-30 years) and are not accessible to the public except through a Freedom of Information Act (FOIA) request. Read about access to State Dept.records in the guide linked below.
"In general, permanent records 25 years and older, pre-1925 passport and pre-1940 visa records are property of the National Archives and Records Administration (NARA)." Generally speaking one must visit NARA to view their records.
Please note that a good number of NARA's records are available in microfilm. UVA Library owns copies of many of these titles (see sample list). It's possible to purchase or to borrow through interlibrary loan microfilm titles not owned by UVA.