一番日本の味に近いって英語でなんて言うの？

This food is so close to authentic Japanese food.
This food is excellent! It is nearly identical to true Japanese food.
I have not found another restaurant that makes such authentic Japanese food as yours.
You have the best Japanese food I have tasted abroad.
My compliments to the chef. This is superb Japanese food. Almost authentic.
This is the best Japanese food I have tasted outside of Japan.

"This almost tastes like authentic Japanese food!"
"almost" meaning that the taste is very near to the Japanese flavors

"This is very similar to real Japanese food!"
"similar" meaning, not 100% the same taste but close

"This foreign restaurant serves really good Japanese style food!"
"Japanese style" meaning that it is not made by a Japanese person but they cook Japanese food

Authentic means it is done in a traditional way as in that country and origin and is very like traditional Japanese food
A simple way to espress this is 'the food here tastes just like it does in Japan'

1.
Saying that one has tried a place is a way to indicate that he/she went to the restaurant in order to experience the type of food that it serves. The "genuine thing" expresses that the food is very similar and almost identical to the food served in its original location.

2.
In order to indicate that one has experienced the real and original thing (Japanese food in this case), saying "as authentic" is a way to express that. In order to make a point to explain that one is speaking specifically about restaurants that are outside of Japan, it is important to say "while traveling abroad."

While talking about a certain Japanese restaurant (abroad) and also the fact that you have eaten at many Japanese restaurants (abroad) before, you want to say that this restaurant is the closest to the real authentic Japanese taste. Either of the above suggestions is adequate for that scenario.