How to safely move all my Picasa folders to another drive

If all your folders are sub-directories of Camera from within Picassa right click on Camera and select move folder. Select destination and that's pretty much it.

Try Move Pictures Without Rescanning from the PicasaStarter Users Guide:
(PicasaStarter is a 3rd party tool for multiuser and portable Picasa picture management)

1. If the new database is not already defined, make a new database as a copy of the database for the Pictures to be moved.

2. Select the new Database on the destination drive that will be the database for the moved pictures, then click the "Run Picasa" button and you should see all your pictures and albums unchanged so far.

3. In the Picasa View Menu go to Folder View and set it to Tree View so you can see where the folders you are moving come from. Any folders that are already on the Portable or Network drive don't need to be moved!
4. In the Folders list on the left side of the Picasa Window, find the containing folders for the pictures (for instance "Vacation Pictures" and click on it to be sure it is the right one (It has the pictures and subfolders you have in that folder).

5. Right-click on the containing folder name in the folders list. Select "Move Folder" from the drop-down menu.

   Picasa Right-Click on a Folder then Click on Move Folder...
   

6. Select the location to move the pictures to in the directory list. This should be the folder you are moving the pictures to on the destination drive.

7. For instance if you are moving all the pictures in the MY Pictures folder to the Pictures folder on the P: Drive, this would be the folder called P:\Pictures.

   Select Location to Move Folder To
   

8. This moves the containing folder and all subfolders to the new location. Reminder! If the folder contains other things such as documents they will also be moved! so it might not be the best idea to try to move the My Documents folder!

9. Picasa will now be busy for a long while because it has to copy (actually move) all the pictures to the destination drive, and it has to change all the drive letters in the database. Picasa will not rebuild the database or change the face names or albums. After this is done, you have the pictures and database in the new location.
10. Repeat the above move folder procedure on the remaining folder(s) to be moved. Make sure any remaining folders you move have not already been moved by right clicking on them and clicking the Locate on Disk option to see where they are on the computer before doing the Move Folder option. DO ALL MOVING IN PICASA, OTHERWISE THE DATABASE WON'T BE UPDATED AND THOSE FOLDERS WILL BE RE-INDEXED!!