1. To move to higher ground, as in preparation for or in response to a natural disaster. There are bound to be tidal waves after an earthquake like that. We'd better run for the hills!

2. To flee hastily; to clear out or depart quickly. Uh oh, Uncle Jerome's been drinking again. Run for the hills, everyone! The staff all ran for the hills when it was announced that there would be a stock-take at the end of the shift.