My renter moved out and left a lot of her things at my place. She told me that she would pick up her things on a specific date and did not show up. I have contacted her several times and told her that I need her to get her things asap since I am not her free storage unit. How long do I have to keep her things before I can get rid of them?

It will vary by location, I do one of two things for my rental, I consider the rental still "rented" and they will be held liable for rent till their things are picked up. I bet they will pick them up faster if they think you will keep charging rent.

The other I move their items to a storage unit, pay the first month and inform them of the location and mail them any info for access ( codes, copy of pad lock key ** cheap lock)
If they don't pick it up, and the pay the storage.

Of course most of my leases or rental agreements ( too late for this person) will say that any items left after they move out, will be held only as long as rent is paid, once they vacate rental unit any property is abandoned and will be held for only 10 days. ** make sure what you do follows your local and state laws.