Go to Hotel New Otani for a quick session
Seisei-an Tea room in Hotel New Otani offers a quick an casual tea ceremony experience program. It is nothing too strict or stiff. The tea master is very frank and talkative. Since it is organized per request, usually very small group, maybe just for yourselves. It costs only 1000 yen plus tax and I guess it is quite reasonable for those who just want to have a feel for it.