Being surrounded by the stillness of night brings a peaceful, relaxed feeling.

Literal

Night [gen-の] stillness [gen-の] inside [in-に] am-[cond-と] peaceful-[and-で] relaxed feeling [to-に] becomes.

A gentle, reflective sentence typical of introspective writing. 静けさ ('stillness, quiet') is the noun form of 静か. ~ていると expresses habitual/conditional ('when I'm in X, then...'). The chain 平和で安らいだ気持ち shows how na-adjective and past-tense-adjective can combine to modify a noun: 平和で (te-form of 平和だ, 'being peaceful') + 安らいだ (past form of 安らぐ 'find peace,' here stative).