For all the other Adobe apps when I go to save I see two options, local computer or CC. But for InDesign, it only shows the local computer. How do I save my documents to the cloud to be able to access them on another device?
You need to clarify what you're trying to do. There are many different cloud services. You CAN save InDesign files to many different cloud services. Look at my screen capture: This shows circled five different cloud services I have that you can save to (more are possible):
You may be referring to Photoshop 2021 or Illustrator 2021 which have allowed their files to be saved to Adobe's cloud in their Save dialog to make it easier to exchange files with versions of those applications on an iPad. InDesign cannot be used on an iPad. (This technology can also be used for other purposes.) That particular kind of cloud usage has not yet arrived in InDesign, although it's like it will happen in the next year or two (my guess).