There are a few varieties of large roaches (1.5-2 inches long) found in warmer climates and they all have a few things in common:
- They eat decaying vegetation outside.
- They are drawn to warmth and moisture.
- They can get into buildings through open doors/windows or those without intact weatherstripping or through small cracks around pipes/vents/roofing into the building.
- They are most likely to invade when it gets cooler outside than inside and/or when it gets dry out and there's a water source inside.
- They may get into open fresh food items found in a kitchen but they actually prefer decayed food so they are not drawn indoors for food.
- Some can fly; some cannot.
- Some scatter when the lights come on; others do not.
- They may sometimes be found indoors in large nested numbers but usually, any that are found indoors are SINGLE individuals that have made their way indoors temporarily, as they (thankfully) prefer to nest outdoors in proximity to decaying piles of leaves.
The smaller (up to 1 inch long) northern German cockroaches are more likely to spread germs and become an infestation problem because of their habits:
- They are drawn to both fresh and decayed food indoors.
- They DO scatter in the light and hide more quickly due to smaller size.
- They are also drawn to warmth and moisture where it's greater indoors than out - a problem in the cooler north.
- They reproduce more rapidly and frequently than their larger cousins.
- They do NOT fly.
- They are rarely found alone and usually (unfortunately), when you find one indoors, there's a whole population nested in the building's walls nearby and very hard to completely kill so none are left to reproduce.
Quality resorts and hotels in FL will spray the perimeters of their buildings on a regular monthly schedule to minimize the invasion of any palmetto bugs, ants or other insects. With many, many FL vacations behind us, we have only found an occasional dead palmetto in the foyer near the front door, so they must have come in through the crack under the door, then died after crossing through a treated area. If one is ever found live indoors, it may have flown in when the door was open.

Haven't had that happen to us.
Some pest control websites recommend that southern homes avoid incoming Palmettos by sealing well around window frames, pipes, cable/electrical entry points and keeping good weather-stripping around all doors and sliders. Brand, spanking new buildings may not yet have had all the fine detail sealants applied nor the earliest pesticide treatments. Much, much older buildings may not have had adequate upkeep to their sealant maintenance. So the better bets may be buildings that are relatively newer and well-managed and maintained.
Palmettos are more active in warmer weather. They don't like the cold. While less active and fewer in number during the winter, they are drawn to the warmth indoors. So for people who fear them coming inside, as a visitor, consider coming to FL or the southeast in a reasonably warm season (spring, summer, fall) and putting your AC on high to keep your room cooler than the outdoors and to dehumidify your room. This can make your room less appealing to them and if they do get in anyway, they'll be inclined to keep going, head out and move on to a warmer, moister place.

Also, if you happen to spot a single live one inside, it may be killed by squashing or a good shellacking by a strong (Aqua Net type) hairspray. Once a lone one is dead or departed, at least you really don't need to worry about there being lots more hiding as that's quite unusual and you'd likely hear of a problem like that on these forums.
Mikethern/OP, these critters give me the willies but I don't give them a thought when they're not right in front of me. However, a phobia is, by definition, an irrational fear which is very real to the person. My hope is that with this info, you'll be better able to deal with it and it won't interfere with your having a WONDERFUL vacation in FL or in the south.

HTH!