Don't forget to send that letter tomorrow, okay?

Literal

Not-forget-[without-ず] tomorrow that letter [object-を] send-[request-て] [tag-ね]

手紙を出す — literally 'put out a letter' — is the idiomatic way to say 'mail a letter' in Japanese; 送る can also work but 出す is more colloquial. The sentence-final ね turns a bare command into a soft check-in, inviting the listener's acknowledgement.