adjective
BAD : I cannot give you the accurate date of my arrival yet.
GOOD : I cannot give you the exact date of my arrival yet.
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Accurate is mainly used (1) to describe something said or written that contains no errors: 'Her novels are always historically accurate.' 'These figures can't be accurate, surely.' (2) to describe something that produces no errors: 'Are you sure the bathroom scales are accurate?'
When you mean 'correct and as detailed as possible', use exact : 'The exact time is three minutes to seven.' 'Do you remember his exact words?' 'They'll be arriving next week - on Friday at three, to be exact.'