She's leaving for Kyoto the day after tomorrow.

Literal

Day-after-tomorrow, she [topic-は] Kyoto [toward-にむけ] depart [polite-ます].

~にむけ (or ~に向けて) = 'headed for / aimed at' — a compound particle for destination or target. Slightly more formal than plain に for destinations. 出発する is the Sino-Japanese verb 'to depart.' Travel announcement register.