Although traditionally Tokyo did not have Onsen, today there are few Onsen within metropolitan area of Tokyo.

Onsen referrers to natural hot spring, not just hot water spa with public bath. Tokyo does not have natural hot springs which is sprawling from ground naturally, but today we can dig down so deep into the ground to find hot water very deep underground.

Ooedo Onsen Monogatari at Odaiba, one of famous and popular in Tokyo. This is like large amusement for Onsen, not just dipping in hot spring tub. The price reflects that.

Time Spa Resta (looks like website is Japanese only), near Ikebukuro at Sunshine City. Open from 11:30 a.m. to 9:00 a.m. The price is not much different from Ooedo Onsen Monogatari, but this facility is 18 years or older only. More quiet atmosphere.

Utsukushi no Yu (again, website in Japanese only). Right near Takaido station of Inogashira line (from Shibuya). The difference of this place compare with above two is the price. Above two can be more than 2000 yen per person, but this place is 900 yen per person weekdays and 1200 yen per person during weekends.

If you are looking for more traditional Japanese Onsen atmosphere then I recommend a day trip and get out from Tokyo.