Can I visit the Trinity College (Cambridge) library and see some of their rare books: Newton Principia, Ramanujan, etc., as displayed in the "The Man who Knew Infinity" movie?
The Wren Library of Trinity college is open to the public from noon to 2pm each weekday throughout the year and also from 10:30am to 12:30pm on Saturdays during university "full term". It's closed at Christmas and Easter.
Their website says, "There are six exhibition cases in which a small fraction of the Library’s treasures are on display" but it doesn't give more precise information. You could ask the Trinity College sub-librarian what is currently on display; their email address is included on that page.
I expect that Newton's copy of Principia would normally be on display because it's so famously associated with the college. However, it's currently (until August 2019) on display in a public exhibition at the University Library, which is open 9am–6pm Monday–Friday and 9am–4:30pm on Saturdays.
The Wren Library's Ramanujan collection has been digitized and is available online. Of course, that's not the same thing as seeing the original documents. Newton's Principia and Opticks are also online.