You've probably received a response to your query by now but just in case...
-- Calvary Catholic - Graham Ave. - deeded: 1865 -- Hillside - S. Wisconsin St. - 1st burial: 1859 -- Oak Grove - E. North St. - 1st burial: 1844
Hillside and Oak Grove cemeteries are in the city Whitewater, Whitewater Twp., Walworth Co., WI.
Although "in" Whitewater, Calvary Catholic Cemetery is actually located in Cold Spring Twp., Jefferson Co., WI.It is supposedly one of two private cemeteries located within the grounds of a university campus (the other is St. Patrick's Cemetery on the campus of Bolwing Green State University in Kentucky).
Therefore, I'd guess the "old cemetery" as Oak Grove.