Since its original 1961 opening, the Suntory Museum of Art has subscribed to an underlying philosophy of lifestyle art. Rotating exhibitions focus on the beauty of useful things: Japanese ceramics, lacquerware, glass, dyeing, weaving and such. Its current Tokyo Midtown digs, designed by architect Kuma Kengō, are both understated and breathtaking.
Check its website for discount coupons for admission. Usually on Thursday afternoons it hosts tea ceremony demonstrations. There's also a good shop and cafe here.