There are two stories in Archie and Me Comics Digest 8 (August 2018) where Archie and the gang go the the Riverdale Public Library.
The first is “The Long and the Short,” which I think was originally published in Jughead 8 (1988). The library angle in this story is secondary to the main plot, which is about Jughead correcting his friends’ vocabulary, but it begins with Archie on his way to get more books, because it’s summertime and he wants to do a lot of reading. For our purposes it’s interesting because the library’s exterior here is different from other stories:
Notice the video shelves in the background on the left. Borrowing videos from the library was pretty important in older Archie stories.
This entrance is different from any other I remember:
“The Long and the Short” was written by Frank Doyle, pencilled by Doug Crane, inked by Mike Esposito, coloured by Barry Grossman and lettered by Bill Yoshida. It is copyright Archie Comics Publications.
The other story is “Castles in the Sand,” two-parter originally from Archie at Riverdale High 104 (1985). Archie is out at the beach and gets challenged by kids from Oceantown to a competition to see who can build the best sand castle. His first stop is to do research at the public library.
Looking through issue after issue of a newspaper is a very tedious way to find something. Full-text searches of back runs are available for most major newspapers now and would make this but a moment’s work.
This story was written by George Gladir, pencilled by Stan Goldberg, inked by Rudy Lapick, coloured by Barry Grossman and lettered by Bill Yoshida. It is also copyright Archie Comics Publications.