There is a good list of onsen and sento in and around Tokyo here: http://www.timeout.jp/s/en/tokyo/feature/536/Tokyos-top-onsen
To be honest although many onsen have that rule I've never seen it enforced. Usually you see at least one person with tattoos on a trip to a day onsen. I went to Shimizuyu the other day and would recommend it as a nice onsen and one of the rare ones with fresh, non-chlorine, non-recycled spring water (in the yellow colored bath). Just checked their site (Japanese only) and no mention of tatoos, but may be worth using their contact form or sending a short message via their Facebook page to check.