I agree the Fire Museum, the Mand Library and the National Fire Heritage Center. I'd also add the National Archives and the Smithsonian in WDC and the American Museum of Natural History, the Museum of the City of New York and the Metropolitan Museum of Art, all here in the city. They each have a highly-respected appreciation for heritage and a passionate commitment to passing that along to future generations.
It hurts me to see some of these items tossed off on eBay. Artifacts of such extraordinary intrinsic value MUST be treated with well-deserved respect and preserved, along with their stories, for many future generations. No matter your age or health, don't leave them to the whims of your heirs. Tag, photograph and catalogue them, write why they are important to you with each item's history and list them in your will along with your desired disposition.
Just some ideas.
And thank you, everybody, for your responses to my original question.