Since you mentioned Austen, a few classics that are in some ways similar (historical fiction, primarily concerned with relations and connections between people, and more or less "clean": Edith Wharton's "Age of Innocence", Ivan Turgenev's "Fathers and Sons" (we discussed that one in the Russian book club a few months back, everybody who read it liked it a lot), Evelyn Waugh's "Brideshead Revisited", Kazuo Ishiguro's "Remains of the Day" and "Never Let Me Go" (also a recent book club discussion). I'd like to add my current favourite author A.S. Byatt (particularly for "Possession" and "The Children's Book", but most of her books do have at least some sex scenes, not in a smutty way but sometimes explicit enough that you might be uncomfortable.