、。
With a deep sigh, I head for the hallway.
Literal
Deeply-[mimetic-と] sigh-do-[and-て], hallway [toward-へ] head.
Narrative present-tense prose, typical of first-person fiction. 深々と is a doubled-kanji mimetic for 'deeply, profoundly' — the reduplication intensifies; it's used adverbially with と. 嘆息 ('a deep sigh, lamentation') is more literary than ため息. The historical present (dictionary form for narrative action) gives an immediate, in-the-moment feel. ~へ marks direction of movement.