。
She arranged to meet him at a coffee shop.
Literal
She [topic-は] coffee-shop [at-で] him [with-に] meet [attributive] promise [object-を] did.
約束をする ('to make a promise / set an appointment') is the standard light-verb pattern — many abstract noun + する pairs in Japanese can also appear as noun + を + する with the noun made explicit, slightly emphasizing the act of arranging. Note the relative clause 彼に会う ('to meet him') modifying 約束 — the verb 会う takes に, not を, for the person being met (since 'meeting' in Japanese is conceptualized as 'going to' someone rather than 'doing' them). コーヒー店 is one of several names for coffee shop alongside 喫茶店 (the older, more traditional kissaten) and the modern loanword カフェ — 喫茶店 carries more of a Showa-retro flavor.