Tour guide quests....help me out here

Make sure you are out of combat mode when running. That way you will auto-heal, and won't need to waste time getting out of combat mode when you reach the automaton. Double click the automaton to register your visit. You will probably then die, and become a ghost. Look at your compass, which should show you the locations of various ankhs. Head for whichever has the largest icon (that's the closest one).

Rinse and repeat for the other three quest locations.