〜な雰囲気って英語でなんて言うの？

Atmosphere is the correct word. You could also use the word ambience to mean the same thing, for example "I love this restaurant, as it has a great ambience."
A more colloquial way of saying this would be to say somewhere has a good "vibe". "i love this restaurant, as it has a great vibe!"
In terms of traditional atmosphere we often use the word feel - short for feeling. "Nara prefecture has a traditional feel."

>Environment
the setting or conditions in which a particular activity is carried on.

>Aura
quality that seems to surround and be generated by a person, thing, or place.

>mood
the atmosphere or pervading tone of something.

Example sentence
a. The restaurant has a nice environment.
b. That restaurant has a great aura
c. The restaurant has the perfect mood.

You can also environment instead of atmosphere.
Environment means the surroundings or conditions in which a person lives or operates.

You can also say "The restaurant has such a good mood."

Vibe =A distinctive emotional atmosphere; sensed intuitively. A shortened form of 'vibration.'
"It gave me a nostalgic vibe".
"That man gives off bad vibes."

Ambiance
= the character and atmosphere of a place; atmosphere, air, aura, climate, mood, feel, feeling, vibrations, echo, character, quality, complexion, impression, flavour, look, tone, tenor, spirit;
"The relaxed ambiance of the cocktail lounge is popular with guests."

"Ambience"
"Aura"
"Tone"
"Ambience" can be used as it describes a feeling of relaxation. "Aura" describes the distinctive feeling of warmth in your surroundings. "Tone" is color and setting of decoration that gives the restaurant a great feeling of warmth and gives it a good vibe.

The restaurant has an amazing ambience.
The restaurant has a wonderful atmosphere.
The restaurant has good vibes.