Fortunately, I have a friend who is an expert, and she kindly allowed me to post her top 3:
Mandarin Oriental Hotel in Nihonbashi:Let me know if you have any favorites!
My favorite place with delicious scones. ;q Outstanding service with stylish and unique oriental tea sets. Very comfortable and I always end up staying there from 5 hours straight (12pm through 5pm)!
Park Hyatt Hotel in Shinjuku:
Modern, classy atmosphere with nice view. Great selection of tea, and all-you-can-eat style sweets. (It's not a buffet; hotel staff will deliver varieties of sweets to your table.)
Palace Hotel in Marunouchi area:
They have a cozy terrace by the water of the imperial palace moats, and their sweets are very unique with some Japanese touches. They even offer Maccha as a part of the afternoon tea set. They do not accept reservations however, so it's better go early before tea time at 2pm.
I can't find any afternoon tea music, so I leave you with a British singer, Kyla La Grange: