How about something different?
The Happiness Project by Gretchen Rubin
Here are some more suggestions, all of which my daughter really enjoyed:
CONTEMPORARY FICTION:
Sweetness at the Bottom of the Pie (Flavia de Luce mystery) by Alan Bradley - fun, silly lighthearted mystery featuring a nine-year-old chemist sleuth.
Americanah by Chimamanda Adieche Ngozi (sp?) – a very well-written, fun look at race in modern America, from the point of view of a Nigerian immigrant
Kite Runner by Khalid Housseni – Needs no explanation
Kindred by Octavia Butler – A modern African-American woman time travels to the antebellum south. A little cheesy and overly dramatic, but good for young adults. (came out in the 1970s, I think).
Tenth of September by George Saunders – weird and wonderful short stories. Highly literary, but I think they are accessible enough for a 20-year-old to enjoy, even a non-reader
The Love Affairs of Nathaniel P by Adelle Waldman – A look at love in contemporary hipster Brooklyn. My twenty-year-old daughter loved it.
The Namesake by Jhumpa Lahiri – Wonderful tale of multiple generations of Indian immigrants. Might be too literary.
When the Killing’s Done by TC Boyle – Super interesting and well-written account of the battle between the environmentalists and animal rights activists over Santa Cruz Island (one of the Channel Islands off of Santa Barbara). A quirky choice, but one that deserves more attention.
CONTEMPORARY NON-FICTION:
Fun Home by Alison Bechdel – graphic novel about a young lesbian making sense of her childhood and her relationship with her father. Superb. One or two sexually explicit drawings, if that is a concern.
Wild by Cheryl Strayed – A young woman goes on a month-long solo hike on the Pacific Crest Trail as a way of turning around her life and dealing with the grief from the death of her mother.
Bossypants by Tina Fey – hilarious memoir by the comedian.
Me Talk Pretty One Day by David Sedaris – Hyperbolic essays by the master of the form.
Any of the Bill Bryson books – accessible and enjoyable history, in anecdotal form
Truth and Beauty by Anne Patchett, along with Autobiography of A Face by Lucy Grealy – two accounts of many of the same incidents
A FEW LIGHTHEARDTED CLASSICS:
Right Ho Jeeves by PG Woodhouse – good silly fun
A High Wind in Jamaica by Richard Hughes – classic adventure story of kids who are abandoned to a crew of misfit pirates
A DECIDEDLY NON-LIGHTHEARTED CLASSIC THAT IS ACCESSIBLE AND GREAT FOR 20-YEAR OLDS:
Grapes of Wrath by John Steinbeck – My 20-year-old daughter’s all time favorite book.
I had to read Americanah for school – definitely agree with that recommendation. Very well-written book.
Correction to prior post: The George Saunders story collection is Tenth of December (not Tenth of September).
Given that she liked Pride and Prejudice, has she read any Edith Wharton? House of Mirth is an all time favorite of mine.
The Bronze Horseman trilogy has a very large young adult popularity. I love it.
Does she like alt fiction (think of shapeshifters and such )…the Anne Bishop books (starting with “Written in Red”) are really well written books, it is a kind of dark fantasy, it is a world where humans are not necessarily the top of the food chain, bit dark at times, but pretty well written. In a similar vein are the Kate Daniels books by Ilona Andrews, lot of humor in it, good characters, but it also has a dark side. Patricia McBride’s Mercy Thompson books are another series in the same vein as well.
Mindy Kaling’s “Is Everyone Hanging out Without Me”
I conveyed some suggestions to H, and he asked me about All the Light We Cannot See. I read it a few moths ago, and he apparently read part of it while it was here. (I also gave it to my mother for Christmas, and she loved it, but my mother is a serious bookworm, like everyone on my side of the family. 
)
That’s what he decided to send. I guess that he wanted something more “worthwhile” than purely entertaining. We’ll see how that works out!
But thanks for all of the suggestions. I will keep them in mind in case he wants to send another book for Christmas.
Good choice, @Consolation!