One strategy for doing this would be to move the folders on disk while Lightroom is closed, and then open Lightroom and tell it that the photos now exist in a new location. Once Lightroom knows about the new location, it will update the catalogue references for those files so your metadata and settings for the photos remain intact.
When you've moved an entire directory from one disk location to another, and it no longer exists in the previous location, you can right-click (on Windows / ctrl-click for Mac) on the directory name in Lightroom's navigator and select "Find missing folder". Lightroom will pop open a dialog box for you to browse to the new location of this folder. If my memory is correct, this should also update any sub-folders that Lightroom knows about and still exist in the parent directory, but if not, you can also update them individually using the same method.
Lightroom also has a process for identifying individual photos that have been moved to a new location. In this case the photos will have a small exclamation mark in one corner to indicate that Lightroom thinks it's missing. Click on the exclamation mark and select "Locate", then you can browse to the new location of the photo. You should also have the option to "Find nearby missing photos" in the location dialog box this time. If you enable this, Lightroom will also scan this folder for other photos that it has determined are missing from the original folder, so that you don't need to repeat the process for each one.