Would anybody know a hotel in the Ebisu / Meguro / Shibuya / Yoyogi Uehara / Sangubashi areas featuring tatami rooms?

Hi GTR88 and welcome on board ! :)

One of the most famous hotel with japanese rooms (tatami) is the Meguro Gajoen, in Meguro:

http://www.megurogajoen.co.jp/english/guest.html

You also have some western hotel with japanese rooms, like the Four Seasons Chinzan-So, but the price will be expensive (suites).

If you're not looking for overpriced rooms, but reasonable prices, you can try some ryokan inside Tokyo:

Tokyo Ryokan, in Asakusa.

Ryokan Kangetsu

Sawanoya Ryokan

And Andon Ryokan, if you're not against some "modernism" in the rooms.

Hope this helps !

Welcome on board friends .
Claska is a unique hotel in Meguro specially known for its tatami rooms. I must say that you should try this if you are going to Meguro...
Recommendation to all the friends who are planning to be on roads towards Meguro.

http://advance.reservation.jp/hotel_claska/stay_pc/rsv/index.aspx?hi_id=1&lang=en-US