Usually, before taking a Road Trip it's good to know where you are going, or at least in which direction. I decided each of my destinations through a different thought process - I went to Chicago just because Chicago is cool, I went to Colorado because I love the mountains, I went to St. Louis because of a coin toss, and I went to Vegas to escape the cold weather in Iowa. Usually there is some motivation - some reason why you want to go to some particular spot. Choosing a destination is a somewhat personal decision. It's not usually too important, though. The whole country is waiting for us - there are hundreds of new and adventurous things to do almost anyplace in America. Choose a destination that suits your personality and mood, and you'll have a great time.
If you don't know where you want to go, just pull out an atlas and start flipping through the pages until you find something cool. I highly recommend the Rocky Mountains, and Chicago is a fun city. Albuquerque is beautiful at night when coming into the city from the west on I-40. Las Vegas is a great town with a cool night life. Miami is warm during almost the entire year, although it is a bit rainy.
If you already know where you want to go, it might be beneficial to check out my resources above. I've got links to check the weather, and find the best route to your destination.
If you plan on taking a Road Trip to a far away destination (>750 miles) you will probably want to plan it a few days in advance. I recommend recruiting a co-pilot and crew, deciding when you're going to leave, where you plan on going, what you want to do there, etc. If the weather is marginal, keep yourself updated on changing weather with the internet. Keep the trip in mind for a few days before you're going to leave, and think about what you're going to take. You might want to make a list. I start packing stuff about an hour before we leave. I usually don't do much planning for shorter Road Trips (<700 miles.) I like the spontaneity of jumping in the car and driving a few hundred miles.
Once you get to your destination, keep in mind that you are there to have exciting adventures. If your crew members are irritating you, don't let it bother you; just concentrate on having fun. Don't be shy or afraid to talk to the locals - they're the people with intimate knowledge of the surroundings. Ask the gas station attendant for her favorite place to go for a mountain hike, or ask the cashier at McDonald's for exciting local activities. Try to develop a good feel for cool activities that aren't real 'touristy'. We aren't tourists, we are Road Trippers!
Here are some cool destinations that I ripped from some Road Trip page:
