There are several ways to move files inside Media Center. Doing so inside MC instead of using Explorer, for example, will allow MC to update its library to reflect the move.
Library Tools / Rename Files from Properties
Using Library Tools, Rename Files from Properties, you can use the renaming to move your files.
1. Select a few files to test before you do many. 2. Check the Directories box. 3. Set the "Base Path". This is the folder under which your music will be stored. Example: C:\Music 4. Set "Rule". Example: [Artist]\[Album] will make a directory named for the Artist and a directory under that for each Album.
Once you've done this for the selected fiels, you'll see the proposed results on the right. Hover your mouse over one or two lines to make sure it's going to do what you expect. Then press "OK".
Library Tools / Find and Replace
Find and Replace will let you change any part of any field. If you do this in "File Location", you can change, for example, "C:" to "D:" or "C:\Music" to "C:\Video".