1- Sur Balik Arnavutkoy:

Located on the European side of the Bosphorus in Arnavutkoy district which is one of the most lovely districts in Istanbul with wooden houses and the beautiful view of the Bosphorus in front. You will find there a lot of beautiful luxury restaurants like Sur Balik where you can enjoy tasty seafood and drinks, amazing view, and calm atmosphere. Sur Balik offers both classic and unusual seafood dishes in addition to wide choices of mezes, all of its fish and seafood are seasonal and fresh, and the wine collection is excellent there.
Make sure to bring a fat wallet with you, it is going to cost you extra dollars.

2- Rumelihisari Iskele:

One of the most famous restaurants at all. Located in Sariyer right on the Bosphorus and has been serving customers since 1992 this is why it has such a good reputation. At Rumelihisari Iskele you can have a delicious seasonal fish dish in a calm relaxing atmosphere and lovely view of the Bosphorus second bridge. The service at this restaurant is always rated 5 stars.

3- Uskumru:

An exceptional restaurants that can be reached by boat, you can have your meal in the sea and literally touch the water with your feet. The appetizers there are superb and creative, sea bass with basil, walnuts, squid a la plancha and many other appetizers and of course the seafood is seasonal so make sure to go there between may and october at the day time for an experience.
And a fat wallet also..

4- Balikci Kahraman:

It is a family run restaurant named after its owner, it serves Black Sea fish and seafood and the mezes there with the lovely atmosphere are what make it a successful restaurant. Kahraman restaurant is the preferred restaurant for celebrities because it is far from the city center, calm and serve great grilled fish dishes.

While if you are looking for cheaper restaurants with same tasty seafood, you can visit one of the following restaurants:

5- Tarihi Karaköy Balikçisi:

Its name explains how old this restaurant is Tarihi ( Historical ) Karaköy Balikcisi has been serving since 1923. From that time until now, nothing has ever changed in its service or great food. You won’t have a great view, and the restaurant is a little bit small but you will definitely have the most delicious fresh fish meal you ever tried in your life.

6- Ahirkapi Balikçisi:

It is the restaurant where you can avoid paying much money but still in the middle of old SultanAhmet city. You can call it a secret dining that serve fresh fish from a simple menu to local people. When visiting Ahirkapi you will find yourself between loyal citizens drinking raki with a smile on their faces. Small, local,  and serve delicious seafood.

7- Kiyi:

Located on Büyükada, the biggest one of princess islands. With an enormous menu of everyday fresh seafood and fish, Kiyi is considered the best seafood restaurant on Büyükada island. The meze that Kiyi serves is unusual and always fresh, especially green salad. Try to go there during the summer months and day time you will have a great time, and it is not expensive too.

It is important to know that depending on the season, the prices of seafood and fish is variable but always have the same amazing delicious taste, because you are in Istanbul.