The Robert F. Wagner Papers are held at the Booth Family Center for Special Collections of the Georgetown University Library in Washington, D.C. The earliest items in the collection date to 1894, and the latest date to 2001 (it seems one box contains additional items added to the collection after the initial 1949 donation, while everything else dates between 1894-1949). There are actually a dozen different entries in Georgetown's catalog for the "Robert F. Wagner Papers", likely a separate entry for each box of items. Unfortunately, the online entries don't say exactly what each contains, but considering the amount of papers, there are surely at least some correspondence in there. Each entry does have a contact e-mail address for the Special Collection librarian, who should be able to answer your questions. The library also has a separate entry for the "Robert F. Wagner Papers: Alien Files".

When the papers were donated to Georgetown in 1949, several speeches about Wagner were given in tribute. These speeches were recorded. The recordings are held by Georgetown, and have been digitized and made available online. You can hear them in three parts: part 1, and part 2, and part 3. A bit of these speeches is also heard about 23 minutes into this tape, though this might be a duplication of some of the other material. Wagner was still alive at the time of the donation, but he was in ill health, which evidently prevented him from speaking himself. In the 1980s, Wagner's son, the Mayor Robert F. Wagner Jr., was interviewed about the collection at Georgetown, and you can hear that tape here.

Also of interest would be the Robert F. Wagner Personal Papers 1895-1993, which are held in the Institutional Archives of LaGuardia Community College, part of the City University of New York (CUNY) system. The school is in Long Island City, Queens. These are the personal papers of Senator Robert F. Wagner's son (and only child), Mayor Robert F. Wagner, Jr. The entry is a bit confusing, because the description also says: "The Mayor's son, Robert F. Wagner Jr., donated his privately held papers, photographs, mementos, and scrapbooks to the Archives." The mayor's son was actually Robert F. Wagner III, but due to his father's notability, Robert III was evidently also sometimes called Robert F. Wagner, Jr. In any case, with the earliest items in the collection dating to 1895, there must be some items in there that predate Mayor Wagner, who was born in 1910, and instead relate to his father Senator Wagner, born in 1877.

LaGuardia Community College also holds a book called the Robert F. Wagner Collection, which may or may not be the same book held at a few other New York City libraries called the Robert F. Wagner Finding Aid. These seem to relate to Mayor Wagner, not Senator Wagner, but the book(s) may help you find other items/collections related to the elder Wagner.

Another useful collection held in New York City is the oral history of Mayor Wagner, transcribed in 1992. The book is held at the Columbia University Library, and it contains his "recollections of [his] father". Another, earlier oral history by Mayor Wagner is held at the same library, but doesn't give any indication of whether his father is discussed in that one or not.

If you search the Library of Congress Catalog by "Subject", you'll find two collections that contain Robert F. Wagner correspondence. One is the "Emanuel Celler papers, 1924-1973 (bulk 1945-1973)" and the other is "Robert Porter Patterson papers, 1909-1956 (bulk 1930-1952)". Each probably contains an isolated letter or two written by Wagner to each of those men, though the descriptions don't say exactly what each contains.

Another collection you might want to access is the Inventory of the Leon H. Keyserling Papers, 1918-1990 held in the Special Collections of the Library of the College of Charleston, in South Carolina. Keyserling was a legislative assistant to Wagner when Wagner was a Senator, and a couple of the items held in the collection might be useful. One is a letter written by Wagner recommending Keyserling for a job. Another is a correspondence written by Simon H. Rifkind in 1984-85 "referencing dinners and recollections of their work with Senator Wagner."

If you search Worldcat.org through an "Advanced Search" by "Subject", and type in "Robert F. Wagner", you'll find additional library holdings that you may find useful.

I would also suggest you get any biographies on Wagner, or on related people, such as Senator Robert F. Wagner and the Rise of Urban Liberalism by J. Joseph Huthmacher, and Leon H. Keyserling: A Progressive Economist by Donald K. Pickens. The bibliography of each may lead to additional resources.

I hope this helps. Good luck!