I've traveled from Detroit to the Gulf of Mexico with a van full of show cockatiels and everyone made it there well. With show birds you're also concerned about reducing stress (as you are with all birds traveling) but also in making sure they arrive looking gorgeous. It was August so it was HOT!
Make sure they aren't sitting in front of a heater or air conditioning vent, the air blowing on them can make them sick. You can still use climate control inside your car, just don't put the birds in front of the direct air flow. You might want to bring a sheet to help shade the cage from the sun because they can easily overheat from the sun beating through the car window.
My experiences show that they don't really eat or drink much when the vehicle is moving, but when you stop for food or water, let them have some food and water. Removing them when the vehicle is moving helps keep cages rather clean. You can always provide some veggies or greens which also contain moisture so that can be handy when traveling. You might also want to bring a jug of water from home because some water can be different and this might give your bird some digestive upset, but shouldn't be anything serious. Keeping water cups clean is the main thing.
Toys can swing around and can actually injure the birds when the vehicle is moving, so put toys up when you stop.
Many times they enjoy being able to see where they're going but when you go under overpasses they might freak out a little. Anytime something is going overhead they will freak out.
Lights from cars and trucks can be frightening at night when traveling so a dark sheet cage cover can help.
Make sure that your bird flight feathers are trimmed and even so, treat your bird as if it could fly off. Many new things to see on a road trip can spook a cockatiel and they take off blindly in a panic. If they can't get too far, then good. But if your bird is out of its cage and someone opens the car door your bird could very well escape and that is a terrible thing to have happen on a vacation, when everyone is supposed to be having a good time.
One last thought is about filling up with gasoline. The fumes can be toxic. Try to spare your bird the fumes if possible and don't handle your bird after you fill the tank until you've had a chance to wash your hands.
Have fun with your travels and your new traveling companion. We've traveled with cockatiels that liked to sit on the steering wheel when on a straight shot highway. Of course, my husband also had a car accident with a fully flighted cockatiel loose in his car. The car flipped over pulling a small trailer and the bird ended up in a tree and my husband was safe unhurt but tossed to the ground in a median. He amazingly retrieved the bird and everything turned out well. So have fun, be smart, and be careful.