Here's the background on the Stedman Inn:
https://npgallery.nps.gov/NRHP/GetAsset/5c4a70f5-af2c-4fb0-a7ec-6d2d311cb14c with the pertinent reference on pages 31-32 on the PDF.
Albert Chandler, born 1840 in Randolph, served as one of Lincoln's personal telegraph operators during the Civil War and eventually became president of Postal Telegraph and Cable Co. the only viable competitor at the time to Western Union. Chandler returned to his native town to build a summer home in 1886. He named it "Mari-Castle" after his first wife Marilla Stedman, and it stands today at 41 S. Main St. in Randolph
Looks like "Montague House" was built in 1887 (now at the NW corner of Montague Golf Course at the end of Randolph Ave.) for Chandler's friend Robert Kimball, potentially by the same builder of Mari-Castle. The Three Stallions Inn that Brunswick School purchased is east of the golf course with the pool in the backyard.
The effect of the two men can be seen today in Randolph, with the Chandler Music Hall and the Kimball Public Library bearing the names of their benefactors.
Chandler's son Albert Eckert Chandler bought the former Stedman Farm (where his mother grew up) in 1923, which consisted of 50-60 acres NE of the town center, and converted the farmhouse into the Stedman Inn. He once had greater plans back in 1916 to build a million-dollar 200-room hotel on the Stedman land but those plans died during WW1. The younger Chandler owned the Stedman Inn for 4 years, until 1927.
My guess is that the former Walabac was north of the White River, which is the only substantial area "Northeast of the town center" that was likely cleared at the time. It would qualify as a "hillside" as it likely slopes toward the river. I don't think the holes east of Kimball's Montague House (the current Montague GC) would have been this course, even though Kimball died in 1903. The Montague course property was, like today, decidedly East (if not even ESE) of the town center at the time.
Amazing how all these small towns have such a history!