I want to hang out at a location where my ex works
Why do you want to hang out there?
I just want to be close to my ex.
You should not want to hang out near your ex. You are broken up, there is no need to do that anymore.
No, I want to annoy her by hanging out nearby her.
Stop thinking about her entirely. You have no relationship with her anymore, and annoying her will make things worse. Just do something else with your time.