RORY: Fine, but we have a real problem here.
LORELAI: Oh, you think I don’t know that? You think I sit around all day swapping witticisms with Robert Benchley at The Algonquin? No! I am thinking and worrying and using the computer, and I hate using the computer!
Robert Benchley (1889-1945), a humorist best known as a newspaper columnist and film actor. He began writing for The Harvard Lampoon while at Harvard University, before writing for Vanity Fair, and most famously, The New Yorker, where his absurdist essays proved highly influential. He made several appearances in films, and his 1935 film How to Sleep, won an Academy Award in the Short Film category.
The Algonquin Hotel is a historic hotel in Manhattan, which first opened in 1902. It had a reputation for hosting a number of literary and theatrical celebrities, including The Algonquin Round Table (or as they called themselves, “the Vicious Circle”). This group of New York writers, critics, actors, and wits met for lunch each day at The Algonquin from 1919 to 1929, engaging in witticisms which were disseminated across the country through their newspaper columns.
Robert Benchley was one of its most prominent members, and Lorelai is probably referencing the writer and critic Dorothy Parker, previously discussed. Dorothy Parker was a close friend of Robert Benchley, and one of the founding members of The Algonquin Round Table.
[Picture shows a painting of Dorothy Parker at The Algonquin Round Table by Carl Purcell]