She arrives in Tokyo at the beginning of next month.
Literal
She [topic-は] next-month [possessive-の] beginning [at-に] Tokyo [at-に] arrives.
来月の初め ('the beginning of next month') uses 初め (はじめ, 'beginning'). に marks both the time and the destination. 着く (つく, 'to arrive') is the intransitive verb for arrival.