As if the hurricane itself isn't bad enough, these storms have the nasty tendency to spawn tornadoes in their wake.
Tornadoes are by nature more localized than hurricanes, but they're much, much more destructive.
The TV and Radio are your best early warning systems for tornadoes. If the hurricane is spawning tornadoes, you'll hear about it from your TV and radio weatherpeople. They'll let you know if a certain section of the hurricane has spawned tornadoes, and where that part of the storm is moving. You can then plan what you do from there. Of course, the fact that there have been no reports of tornadoes related to the hurricane doesn't mean that you're out of danger.