From Rocklopedia Fakebandica
Lincoln Logs. The 1986 set came with some cardboard signs to spruce up your Old West town, including one advertising "Coming Soon - Singer Annie Day - June 2 — July 21 - Appearing at the Lincoln Grand Hotel."
Don't know if current sets have the sign or not. Don't know if earlier sets had the sign.
The name is some mild wordplay on the phrase "any day."