Not a natural place to bathe, or sail off with a flipping Greek character (8)
I believe the answer is:
solarium
'not a natural place to bathe' is the definition.
(sunbathe)
'or sail off with a flipping greek character' is the wordplay.
'off' indicates an anagram.
'with' says to put letters next to each other.
'a flipping' is a reversal indicator.
'greek character' becomes 'mu' (letter from the Greek alphabet).
'mu' reversed gives 'um'.
'or'+'sail'='orsail'
'orsail' is an anagram of 'solari'.
'solari'+'um'='SOLARIUM'
(Other definitions for solarium that I've seen before include "A room with sunlamps for tanning" , "Room for sunbathing" , "tannery?" , "Sunroom" , "Sun parlour" .)