Safari is a good name for such a trip because like that hunter going into the deep jungle to bag big game, you are going to the unknown to get that perfect photograph. Your preparations have to be expert. Your discipline on the road must be focused. But above all, your determination to get what you came for must be relentless as you hunt the prize you want to bag, not with a gun but with your camera.
One mistake to avoid is over packing for your adventure. It's easy to do because you may have the urge to bring everything in your studio "just in case". First of all, if you have every piece of photography equipment you own with you, the likelihood that something will get broken or stolen is pretty good. So you have to know how to strip down your travel gear to just what you have to have to get the job done.
But how do you know that if this experience is new to you? One way is to do a few "dry runs". Just as you went out and did practice photographs when you were learning your craft, take one or two test trips to the next town. Do these without the pressure of a deadline or a deliverable that you have to complete. An overnighter to take pictures at the zoo in the nearest big city will surface what is needed and what is not. Then repeat the exercise to take photographs out in the country where you may have to backpack your equipment in. You will find out pretty fast what "stuff" is worth the extra weight and what needs to stay home.
Your photography safari is a business trip to you and you have a mission. But your mission is about more than just going somewhere to get a snapshot. Just as every picture has personality and soul, the more you become part of the environment where you are traveling, the better your "eye" will be to capture the perfect photo.
Yes, you must stay focused on the purpose of the trip and stay on schedule. But don't forget to enjoy the trip. If you are going to take a picture of a natural wonder, like Mount Rushmore, for example, spending time visiting with others going to that sight or talking to locals may surface some locations and secrets about the site that other photographers would not get if they just came, snapped a photo and left. Use the "down time" to charm the other travelers and let them charm you. Not only will your picture be a hundred times better, you will have a lot more fun.
Finally, as you reach your destination, your preparations need to pay off and you need to let them pay off. Here is where focus and the eye on the prize is crucial. It is so easy, especially when traveling, to become obsessed with the equipment, with the set up and with your settings.
Do all of that before you leave, or in the hotel room the night before. On location, the session is about your subject, not your equipment. Your equipment is there to serve you. Don't worry about it. Trust yourself that you did a good job getting ready. You have quality equipment and you have prepared the lenses, checked the batteries and done all the right things. It all will work when it needs to work.
Now you keep your eye on the prize. Your expert eyes are needed to judge the lighting, the angle and every aspect of the shot to determine if it tells the story that you know this photograph has to tell. Here is where the artist in you works beautifully with the photographer to produce a photo that you will genuinely be proud of. And if you obey your disciplines and get that shot, it will be a photography safari that comes home having "bagged the big one" to add to your trophy room for sure.