I haven't tried so many unagi restaurants in Tokyo but Unazen 鰻禅 was my best experience.
a the restaurant is located in Oshiage area , between Asakusa and Tokyo Sky Tree.
The place is popular so you should go early and expect to wait in lines. They cook fresh unagi upon customer's order so you will have to wait another 40 to 50 minutes after you get seated! But totally worth waiting. Unagi was so fluffy and tasty. I'd definitely recommend Unazen!