Christine Noble Govan and Emmy West, Lookout Mystery Series, 50's-60's.  This is definately the series you are looking for.  It features a group of kids living in Lookout Mountain, Tennesee,  who call themselves the Lookouts.  The older kids had a group called the Cherokees but they're getting older and not as active in the club anymore.  I'm not sure of the specific title you are looking for in the series.  Here is the list I have:
Mystery at Shingle Rock (1955), Mystery at the Mountain Face (1956), Mystery at the Shuttered Hotel (1956), Mystery at Moccasin Bend (1957), Mystery at the Indian Hide-Out (1957), Mystery at the Deserted Mill, Mystery at Ghost Lodge, Mystery at the Echoing Cave, Mystery of the Dancing Skeleton, Mystery of the Vanishing Stamp (1962), Mystery at the Haunted House, Mystery at Plum Nelly, Mystery of the Fearsome Lake (1960), Mystery at Rock City, Mystery of the Snowed-In Cabin (1961), Mystery at the Shuttered Hotel, Mystery at the Weird Ruins.
Thank you for solving my stumper.  I am most interested in Mystery at Rock City, but would like to collect entire Lookout Club series.  Please let me know if you have any copies or when you get one.  Thanks!

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Govan, Christine Noble and Emmy West.  The Mystery at Shingle Rock. Illustrated by Frederick T. Chapman.  Sterling, 1955, 5th printing.
Ex-library copy in library binding with usual markings.  G.  <SOLD>