My ex girlfriend and I went on a trip right before she ended the relationship unexpectedly. She promised to repay me, but hasn't. Can I sue?

You could seek recovery of your personal property in Small Claims Court. Did your ex put that promise to repay in writing (email)? Was there a pre-trip agreement to share/split the costs of the vacation? If not, a suit to enforce her promise to repay would be a weak claim. There is the possibility that your local small claims court has a mediation program to try to settle this matter prior to a court hearing.