Just following up in AKSAR's good advice, in the case of a locally generated tsunami and earthquake,you might be in the grips of the tsunami before you receive the warning, so, if in doubt, think seriously about doing a little climbing.

Historic precedent would be the Santa Barbra 1812 earthquake,whose epicenter was offshore in the Santa Barbara Channel. It generated a tsunami which reached the steps of the Santa Barbara Mission (not the current mission, but an earlier one at a lower elevation). A little while spent perusing your local tsunami hazard map can be time well spent.