Keep Time Machine from starting in home
I tested this on Mavericks, but this method has worked as far as I can remember. Make sure "Show Time Machine in menu bar" is checked in Time Machine Preferences. Select the directory you want to go to as a Finder window and make it the active window. Select use "Enter Time Machine" from the menu bar Time Machine (small clock) drop down menu. Time Machine will open to your selected directory ready to restore files. If you start at a "hidden" directory you can restore from there.