Coffee cups without a compostable logo (either polystyrene or paper with a plastic coating) cannot be recycled and go in your Landfill Red-lid bin, which goes to landfill.
If your single-use cup has the compostable logo, it can go in your Organics Green-lid bin!
Just make sure you recycle the lid - this goes in the Recycling Yellow-lid bin.
Hint: Buy and use a reusable coffee cup. Your café can make your coffee directly into your own cup.