Hill Air Force Base is located in Utah, a few miles north of Salt Lake City. If you consider Warren a support base for missiles then Hill is a support base for the support bases. Missiles going out into the field are shipped from Hill, and missiles that are pulled from silos are shipped to Hill.
Hill AFB hosted the 4062nd Strategic Wing (Missile) between December 1 1960 and February 20 1962. This was apparently a very short-lived wing and was probably involved in the initial deployment of Minuteman missiles.
Hill has a missile park near the west of the gate entrance that includes a Peacekeeper and a Minuteman III, displayed vertically. See for example http://hilltop.standard.net/archive/19990729/Images, and http://hilltop.standard.net/archive/19991028/missile.html (both links have died). There is also a Minuteman I on display, horizontally, at the Hill AFB Aerospace Museum, see http://www.hill.af.mil/library/factsheets/factsheet.asp?fsID=5718, http://www.hill.af.mil/library/museum/coldwar.asp.
There are three silos used for training of crews and testing/development. One, or perhaps all, are called the Hill Engineering Test Facility (HETF). Location is 41-07-50, 112-00-57. In the photo, the Peacekeeper silo is farthest north, the other two are Minuteman silos. It is currently (11/2007) unclear what the fate of the Peacekeeper facility is, now that the Peacekeepers have all been retired.