You can search the Web for archives. Many archives have an online presence.
Try searching for "Subject" (ex. "Abraham Lincoln" or "Toni Morrison") and "Archive" Once you find a web site, make sure you click on the 'About Us' tab and evaluate the credentials of the institution.
WorldCat, the world's largest catalog, is a great way to locate archives collections.
As an example, see the Clarence Denman Papers, which belong to UTA.
Another good way to explore archival collections is through ArchiveGrid's beta system from OCLC Research.
Another option, especially for seeing which repositories might have uncataloged collections, is to contact the SAA listserv.
Finally, Texas archival collections are available via Texas Archival Resources Online (TARO).