This may sound like an unlikely place, but after my wife passed away, I took several containers of syringes to the Vet's office (Kingwood Animal Hospital / Vitalpet) for disposal and they got rid of them.
I tried to drop them off at the Park & Ride one weekend when they were taking hard to dispose of items, but they refused to take them.
Had to dig deeper but Google says in the state of Texas, after placing needles etc in a plastic container then sealed, you throw that into the trash. Okay. Thought it was odd. But we did just that. Ours are in "official" Sharps Container. I hope nobody gets hurt from this manner of disposal.