This museum has a terrific collection of European art (especially Turner and post-Impressionists), African tribal art, South Pacific art and Chinese works. The complex also includes Oldfields – Lilly House & Gardens, where you can tour the 22-room mansion and flowery grounds of the Lilly pharmaceutical family, and Fairbanks Art & Nature Park, with eye-popping mod sculptures set amid 100 acres of woodlands. Fairbanks, which has its own entrance, is free – perfect for an art fix without the steep admission price.

In summer museum admission includes access to a whimsical 18-hole mini-golf course, with holes designed by local artists.