Places where one might find sheet music for an obscure song include
Ask the person who wrote it or someone who performed it.
On the Internet
Google. In addition to the song title, "sheet music" and "pdf" are good search terms.
Scribd. The Documents section contains many downloadable scores and songbooks. To download a document, register for a free trial or subscribe for $8/month.
Johns Hopkins University's Levy Music Collection includes over 28,000 pieces of sheet music, most from before 1920 but some up to mid-century. Music can be downloaded or (if copyrighted) requested by email.
The University of Mississippi's Sheldon Harris Collection is of sheet music from 1834 to 1967, mostly minstrel songs and blues, not directly searchable, but browseable and downloadable.
The University of Oregon's Historic Sheet Music Collection is of about 1000 pieces, mostly 1900-1920, imperfectly annotated but searchable and downloadable.
Tumblr user MTSheetMusic has some musical theater sheet music and scores.
The Internet Archive has 10,000 pieces of sheet music, most from before 1920.
In a library
The Paul Rose Library, the collection of music and related materials left behind by the great amateur singer Paul Rose, the Club's patron saint. For updates on the Library, join the Friends of Paul Rose Facebook group, or ask Dave to add you to the mailing list.
The San Francisco Public Library's Art, Music and Recreation Center, on the 4th floor of the Main Library. Its collections include
Research assistance is available for free. Assistance with duplication is not available.
The Museum of Performance and Design, in San Francisco's Bayview neighborhood. Its collections (in overview and in detail) include the Bob Johnson Sheet Music Collection of 60,000-some pieces of sheet music and songbooks. A partial catalog of the Johnson Collection is on line. Items in the MPD may be examined on site for for free. Scans of sheet music in the MPD may be requested, including by email, for a small fee.
The Music Division of the New York Public Library's Library for the Performing Arts, in Lincoln Center. Its collections include songbooks kept in the stacks, sheet music on microfilm, and countless rare materials which can be viewed and photographed on site, including the personal papers of some of America's greatest songwriters. A library card is needed to access non-circulating collections; non-residents of New York City can get a temporary card. Paid research and duplication assistance is available, though relatively expensive.
The UCLA Library Special Collections. UCLA has extensive holdings of printed music and related materials which can be searched on line. Paid research and duplication assistance is available, though relatively expensive. Note also the Library's list of UCLA LA Area Music Resource Repositories.
In a store
Hollywood Sheet Music. This former brick-and-mortar music store is now operated on line by a single pleasant, helpful person, Stephanie, who has deep resources and can fulfil requests by phone or email. PDFs run around $7.
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