The establishment in Shibuya which started as a house restaurant has a solid reputation that dates back to the 1930s. Owada now has a couple of locations across Japan. It has a simple menu with the main items being grilled eel on a bed of rice served in a lacquered box. This is called unaju. The prices for those range from ¥3,000 to ¥4,000 depending on the size. The place is extremely popular so you better make a reservation beforehand.
You can also try some other eel delicacies such as this side dish of grilled livers. Despite being in Shibuya, the restaurant has a nice traditional and quiet atmosphere.
Unagi Ichinoya (いちのや)
Ichinoya is a high-end unagi restaurant located in a beautiful traditional building. The unaju (eel on a bed of rice) sets are more expensive than most places but you also get bigger portions of eel. There are some counter seats and also some "ori kotatsu" tables which are low tables over a hole in the floor. The setting makes for a truly authentic unagi dining experience.
Ganso Unatetsu (元祖 うな鐡)
Unatetsu is a restaurant of long standing, well known in Tokyo for its exquisite unagi. The Shibuya location is the "ganso" which means the original location. The place is most known for its skewered types of unagi items. It serves different parts of the eel cooked over a charcoal fire and with either a plain salt or tare sauce (soy base) seasoning. This place is on the cheap side, yet the quality is really good. You can also have the more standard unaju sets. Expect to pay around ¥3,000. for lunch or dinner.
Hanabishi is quite a big restaurant which serves really fine quality unagi dishes. You can have them as part of a kaiseki meal, which is a course meal that includes a many small, exquisitely presented dishes. You might want to try the shiroyaki (plain seasoning) here instead of the standard tare one. It's said to be one of the best. Prices for set meals vary between ¥2,700 to ¥5,200.
Unagi Toku (うなぎ 徳 渋谷店)
Open since 2012, this is a much newer restaurant than the other ones presented. The warm decor is a mix of traditional Japanese and western style. Many unagi restaurants have low tables at which you sit on the floor but Unagi Toku has western tables. The speciality here is a kind of dish called the "Ohitsu Unagi Chazuke" which is a rice topped with unagi served in a round wooden bowl and that comes with a teapot with some savoury eel soup to add to the dish when you want a change of taste and texture halfway through your meal. Prices for this are between ¥2,700 to ¥5,200.