I'm not used to staying up late.

Literal

I [topic-は] staying-up-late [contrastive-には] accustomed-not-[state-ている].

夜更かし ('staying up late at night,' a compound noun). 慣れる ('to get used to, become accustomed to') takes its target with に; the contrastive は inside (には) foregrounds the specific target — 'as for staying up late, (I'm not used to it).' 慣れていない is 'not in the state of being accustomed.'