My area of expertise on First Ladies is focused largely on their political impact, speeches, media relations, policy interests and symbolism. I only have the most limited scholarship on what they wore. However, there are some individual presidential spouses I have conducted indepth research on of whom I've written full-length biographies and there is some information I do know.
Probably the best possible source on Jacqueline Kennedy will be the catalogues of her personal items that were sold at the famous Sotheby's auction in 1996. Perhaps the John F. Kennedy Library in Boston has a copy: not only detailed descriptions but color illustrations of the items.
In doing some general research, I also find items that are now in the museum collections of various presidential libraries and museums: a locket with a miniature painting (I can't make out the scene) given by her husband and worn by Abigail Adams during the long years of their separation while he was serving as a diplomat following his years in the Second Continental Congress.
Julia Tyler, widowed for nearly three decades, wore a painted miniature of her husband, clasped at her throat. As First Lady, she also wore a pearl and diamond string of some kind as a "diadem", apparently a type of headband. You can actually see her wearing it in her official White House portrait. Sarah Polk, widowed for nearly a half a century, always wore an ivory carved cameo of her husband. Mary Lincoln seemed especially fond of a black onyx set of earrings, bracelet, ring, necklace, and pin (it seems to be set with diamonds as well) which she was actually photographed wearing for pictures she gave permission to be released to the public.
Julia Grant most especially loved very green emeralds, very blue sapphires and very red rubies - I believe this is from a contemporary newspaper account of the Victorian era, but like so much written by others (as opposed to documentary evidence from photographs) it may not be true. Ida Saxton McKinley was known to be a jewelry collector, most especially diamonds. Her father and grandfather had begun the habit of giving her diamond rings, bracelets, and it was the foundation for an extensive collection she built over her lifetime. She also seemed to collect jewels that had not been cut or set in metal and kept them in a simple bag that she enjoyed giving to visiting children - to play with!
Nellie Taft also enjoyed diamonds and wore thick neck collars and matching thick (wide) bracelets - almost looking like they were shiny clothing cuffs. She was most famous, however, for her diamond tiara, which she was photographedwearing in the White House. Florence Harding always wore a thick black velvet neckband to cover her wrinkles and the Christmas following her husband's 1920 election, he gave her a large diamond sunburst - as it turns out, unknown to her it had been chosen for him by her best friend, the heiress Evalyn McLean who owned the Hope Diamond. Mrs. Harding in her white diamond sunburst at her neck, and Mrs. McLean with her legendary blue diamond at her neck often appeared together wearing these famous objects. The wedding ring which incumbent widowed President Woodrow Wilson gave to his second wife Edith Bolling was fashioned from a gold nugget given to them by western state citizens.
Eleanor Roosevelt owned a blue aquamarine ring given her by the government of Brazil which she turned over to the federal government since it was a state gift. Mamie Eisenhower was famous for often wearing beautiful costume jewelry, and even pieces from discount stores such as J.C. Penny's and Woolworth's. As a widow, she was rarely photographed without her colored-glass U.S. flag pin. Finally, although she was not as closely identified with it as was Barbara Bush with her three-strand fake pearls (which were copied by several companies and sold as "First Lady Pearls"), Nancy Reagan wore a large and wide gold necklace and bracelet in the latter years of her tenure: she was often photographed in the matching items and even addressed the United Nations in 1988 wearing them.