Compared to earlier versions the local saving of Excel documents has only changed a little. If you have opened a workbook and you will switch into the backstage view - i.e. to file tab - you will find ways to select multiple locations. If you have a OneDrive account or another cloud feature, you can save your sheet also in the cloud, so that others can work with you on the file. If you would like to save only locally on your computer, just click on the computer. This shows you what you have recently used. You can click browse and you will see that you will have the opportunity to select a location and can save your file easily on your computer.
You are able to define the default saving location in the backstage view under options and saving. You can therefore set the computer as your default saving location. In addition, you can hide additional locations, set a local default location for your documents and you can even choose an own location for your personal templates.