。
She promised she'd come see me, you know.
Literal
She [topic-は] me [to-に] come [quotative-と] promised [you-know-よ].
私に来る ('come to me') uses に to mark the speaker as the destination — note that this slightly fixed phrasing is common in Japanese. 約束する ('to promise') takes its content with the quotative と. The clause-final よ adds an assertive, emphatic flavor — 'you know,' 'I'm telling you' — implying the speaker is reminding the listener of something they should know or pushing back against doubt. The whole sentence's tone is slightly emphatic, perhaps even defensive: 'she did promise, after all.'