Guess this City - 7 letter indian city

Guess this City
I am a 7 Letter City.
2,3,4 Letter ia a Bird.
6,1 is Something that Cools.
1,2,7,4 is a Part of the Face.
4,7,1,3 is way of saying Good
4 equal to 5.
Who am I?

Click here for Answer

CHENNAI
234 = HEN
61 = AC
1274 = CHIN
4713 = NICE
4 = 5 = N