It's pretty far, but worth the trip. The Cloisters themselves make for a nice hour-long tour, through which you might ask yourself, "What, wasn't the Middle Ages before America was founded? (You can read the bizarre story here.) But I think their attraction lies in the surrounding gardens and small wood paths. Even the view across the Hudson is unmarred by modern life.
What to bring: A reusable bottle with a secret stash of wine wine, and a copy of Jonathan Franzen's Freedom to read in the shade