Per my hurricane experiences:

Either leave the city early and get out ahead of the herd, or wait 12-24 hrs for the herd to pass and then get on the road. I prefer to leave by highway for at least the first hundred miles and then cross an interstate to see if it's flowing or if it's a parking lot.

You'll want to keep your gas tanks topped off prior to an evacuation being called.

It can be 300-500 miles before a hotel can be found, depending on the size of population that's been ordered.

Camper owners fare best because the daily camping rate is miniscule compared to a hotel daily or weekly rate. Pets are usually not a problem with campsites. (BTW: LaQuinta is a pet friendly hotel chain). Food costs are much cheaper with a camper versus dining out somewhere for every meal.

Plan on several different places to evacuate to depending on the type of threat, it's forecast direction of travel (hurricanes, tornado's), or based on wind direction (nuke accident, wild fires, hazMat incident), and always consider the proximity of extended family and good friends in relation to proposed evacuation locations.