Do you mean a similar genre to Catcher in the Rye or more like art and music biographies?
I second the recommendation for To Kill a Mockingbird. Also second Catch 22 and The Great Gatsby.
Steinbeck is usually popular with people who liked Kerouac. Of Mice and Men is great but short.
The Bell Jar. The Poisonwood Bible. Rebecca. The Man in the High Castle.
He might like some P G Wodehouse stuff - more irreverent and funny.
At 20 I loved Pride and Prejudice but if he has not read many novels then 19th century classics might not be so great to start with.
If he is in the mood for humorous novels then these are not old classics but he might enjoy Good Omens or some other Terry Pratchett stuff. Not funny or a classic but I also recommend The Kite Runner.
On the mid 20th century American music and art track, there is:
Minor Characters: A Beat Memoir
How I Became Hettie Jones
The Holy Barbarians
Which I have heard recommended specifically around the Beat Generation but I have not read them. Then of course there are the actual books/essays/anothologies from the era e.g. The Naked Lunch, Turtle Island.