I won't say this is the 'best' place to get tea in Tokyo, it's just somewhere that I like. I'm particularly fond of the area (Yanaka), it's one of my favourite parts of Tokyo.
It's mentioned on this page: http://www.tokyo-cha.or.jp/entry2007/20070924_1611.html
The list might be interesting to you as it shows lots of good shops in Tokyo
This link is clearer:
And here's a map:
http://maps.google.com/maps?f=q&hl=en&g ... iwloc=addr
(the station to the right is Nippori on the Northern part of the Yamanote line)
This isn't even my favourite tea shop in the area. I'm afraid I don't know the address of that one, just how to find it when I'm there, so I'm sorry I can't share that with you. There are quite a few around. Because the area draws many of Tokyo's older residents and Japanese visitors (there are lots of temples and graveyards) this might partly explain why the tea shops are particularly good here, and the tea sold at reasonable prices.
EDIT TO ADD:
Yanaka is part of a larger area called YaNeSen by the locals (Yanaka + Nezu + Sendagi)
Here's a very nice article with some more information:
(There's even a photo of the tea shop I've recommended, but no other mention)
Lots of photos of the area here: