Mixed saunas here in the Bahamas (6)

I believe the answer is:

nassau

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'in the bahamas' is the definition.
('Nassau' is part of 'bahamas')

'mixed saunas here' is the wordplay.
'saunas' anagrams to 'NASSAU'.
But, I am not clear how this is indicated.

Can you help me to learn more?

(Other definitions for nassau that I've seen before include "Bahamian capital" , "Port of the Bahamas" , "Saunas (anag)" , "Dublin street in the Bahamas?" , "Caribbean resort" .)

I've seen this clue in The Sun.

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