To move the WSUS content folder to a new location, use the wsusutil.exe. It’s located in C:\Program Files\Update Services\Tools\
To move the folder to d:\wsus you first have to create the folder, then run the wsusutil from the command line. Log file has to be specified.
wsusutil.exe movecontent d:\wsus d:\wsus.log
Depending on the size of the local update folder and disk speed, the content will eventually be moved to the new location.
As you can see from these before and after screenshots from the Share and Storage management snap-in in 2008, the util takes care of changing the shares.
I noticed that the utility doesn’t seem to move the updates, but copy them. After the operation was complete, I had to delete the folder C:\WSUS manually (6GB).
More info on storing WSUS updates: http://technet.microsoft.com/en-us/library/bb245839.aspx