well it's not the only way but the best way to get to The Cloisters is by taking the #6 bus on Madison Avenue, which takes you directly to The Cloisters. The #6 bus takes you past through the wealthy Upper East Side, Central Harlem and then Spanish Harlem.
I've always wanted to see The Cloisters! Thanks for making this suggestion. I feel like a lot of the other New York City museums get more attention than this gem. It has a really wide scope in its exhibits. Did you know it's a part of the Metropolitan Museum of Art?
Midtown to The Cloisters It depends where you are staying but if you happen to stay somewhere in Midtown, I recommend taking the Subway because is both cheaper and faster. If you prefer to take the taxi, it will be around $35 there and back, which I think it's way too expensive.