American Antiquarian Society
They collect anything on paper in the United States prior to 1876. They have amazing things!
Creative and Performing Artists Fellowships
Fall deadline: Last year it was mid-October
Tip: They want you to be refer to specific materials in the collection that you're interested in seeing, so you can start exploring the online resources now.
Wellcome Collection Astounding online collection on the history of medicine and health. Plus a library and gallery in London.
Tantalizing Glimpses is a Study Room guide on fat and performance art (or live art) by Charlotte Cooper. It's also a great resource for anyone who has reason to feel unwelcome in an archive. Free to download.
Hawthornden Castle Write and live for a month in a Scottish castle.
For the Hawthornden residency, you have to write a letter to the director, requesting an application form:
The International Retreat for Writers
EH18 1EG UK
The application form has to be submitted in hard copy. (I wrote mine by hand.) You also need two professional references. It's a slow process, so sending a letter asking for an application might make sense even at a moment when it would be difficult or impossible to travel.