Maruya Honten Tokyo Midtown
By far the best unagi I have ever had. The eel is well prepared and tastes great - properly deboned, soft and crispy with plenty of sauce. The unajyu (grilled eel and rice) comes in 3 sizes: 3 portions for 3950 JPY, 4 portions for 4950 JPY, 6 portions for 7850 JPY. The hitsumabushi (grilled eel with rice, dashi and garnishes) is 4650 for 2/3 of an eel, 5850 JPY for 1 eel and 8250 for 1.5 eel. Since the hitsumabushi is sold by the eel, it sometimes feels like a better deal than the unajyu which is sold by the portion (which can vary a bit). The hitsumabushi comes with a small bowl that allows you to scoop out a bit of eel and rice and try it with different garnishes. It is recommended that you eat it the first bowl plain, the second with wasabi, and the third with green onion, seaweed and dashi (soup stock). After that, try any combination that takes your fancy. Please note that refills of the garnishes and dashi are free.
The private rooms have tablets that you can use to order (even the hitsumabushi refills). To pay, take the small wooden plaque with the table number to the front counter. This restaurant is part of Midtown, so it is possible to collect Mitsui points (the membership is free to join) if you are planning to become a repeat customer.
It is recommended to reserve for the weekend and holidays.
Akasaka Fukinuki
For the budget conscious, Akasaka Fukinuki offers a very good lunch deal from 11am-3pm: unajyu is 2200 JPY for a small, 3200 for a medium while the hitsumabushi set is 2500 JPY. They also offer larger sizes (large, extra large, 2 layers) for lunch but the interesting thing is that the sizes refer to the size of the eel which can be very subjective. Having ordered different sizes but unable to tell the difference between my small set and my friend's large set from the size of the unagi, I would suggest just ordering 2 smalls rather than any of the larger sets.
There is usually no need to reserve in advance and there are several locations in Minato-ku. I do prefer the original restaurant (the eel is slightly better prepared) to the newer branch in Biz Tower but both are good. You can collect Mitsui points (membership is free) at the Biz Tower branch.
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Other decent unagi restaurants:
Nodaiwa Azabu Iikura Honten
The medium unajyu is 5000 JPY, hitsumabushi is 3970 JPY. Requires a reservation. Don't order larger size sets - no noticeable difference in size of eel. No photos allowed in restaurant.
Ichinoya
Unajyu small set (5400 JPY for 1 eel), medium set (7400 JPY for 1.5 eel). No reservation required.
Unagidokoro Kurocyodo
This shop has a tank of live eels in the corner. The unajyu is 4800JPY for 1 eel, 7000 JPY for 1.5 eels, 9400 for 2 eels. The eel is very charred (sometimes it tastes like you're only eating charcoal) and the meat is very chewy. It's interesting to try once since the texture of the meat is completely different to other unagi shops and I would recommend it for people who like gamey meat. You can collect Hills points (free to become a member) if you are going to shop often at the Hills Malls.
For my list of restaurants, check out my new map.