Hi GTR88 and welcome on board !
One of the most famous hotel with japanese rooms (tatami) is the Meguro Gajoen
, in Meguro:
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:
, in Asakusa.
And Andon Ryokan
, if you're not against some "modernism" in the rooms.
Hope this helps !