Putting the garbage out Erev Yom Tov is not a problem. You do not need to concern yourself with the possibility that that the non-Jewish sanitation workers will choose to ship the refuse outside of the techum to avoid having an abundance of garbage at hand.

However, the garbage cans are a basis for a Muktza Machmas Gufo during Bein HaShemashos and remain muktza the second day as well. A Muktza Machmas Gufo may not be moved to prevent its getting damaged.