Road trips are just as expensive as you make them.  That being said, with gas prices the way they are, depending on the distance, that is one expense that will be consistent no matter how you do the math.  The other three big things are food, lodging, and activities.  These are the three big ones we will discuss here.
Food: wow food can get expensive quick.  We brought our cooler even though space was limited thinking we would use it for day trips, and the first few months we pretty much didn’t use it for anything besides an extra chair in the dining room.  (We still use it for that).  Before long Chad was telling me we either can’t do that activity or we have to pack a lunch. With eating out running us about $50 a meal it was adding up quick.  We might go an hours drive (or four) to do a free day long outing, but if we ended up paying for two meals at restaurants it was an expensive day.  So we started packing a lunch, and in typical camping style, it was cheaper but not much.  We had to decide if we really want to go out and do these outings, or eat well, and it wasn’t going to be both all the time.  So we eat mostly out of the cooler now.  If we have a four day trip, we will stay somewhere with a continental breakfast so we don’t have to worry about that meal, and we pack our lunches and dinners.  We don’t really eat snacks, but really, do we need to be snacking all the time? Lunches are usually peanut butter and Jelly sandwiches and fruit.  Dinner is usually baked sweet potatoes and more recently cold chicken, baked beans, potato salad, and occasionally hot dogs.  I won’t be able to tell you that this is healthy, plant strong, non GMO, or organic.  We will eat out of the cooler for the whole time besides one meal, and we will pick one meal and eat out as a special treat.  In this way the cost of travel food is already part of our weekly food budget, and not an added expense.
Lodging: We are headed into winter now, which limits the amount of camping we will be doing, but camping, if food is kept to a necessity not buying all of the traditional camping food for a single trip (I’m not saying don’t buy marshmallows, just don’t buy six kinds of chips, boxes of bottled root beer and ribs to grill on the fire all for one trip) can significantly cut our lodging costs from $100 a night to $30 a night.  KOA campgrounds are not usually the most forested or out door adventure type campgrounds, but they are everywhere and even close to big cities if you are trying to stay fairly close to where you will be doing your scheduled activities.
Hotels also come in a wide range of costs.  People are funny about their preferred hotel chains and you are right, there are often big and noticeable differences from one chain to another,  but if you want to travel and make those family memories just figure out what is important for you. This is just one area where there is some flexibility and the choices you make can give you more wiggle room and the opportunity to get out more. We usually opt for La Quinta, mostly because they allow pets to stay for no additional charge, they have a nice continental breakfast, frequently have a pool, are reasonably priced and have a membership type thing that has a stay 10 nights get one free deal, (it’s actually a points system) but if we are staying in a hotel as much as we do, we might as well be earning a free night’s stay.  As soon as the summer weather comes again, we will be out taking advantage of the opportunity to tent it, and be in nature. Oatmeal in the woods is just as good or better than any continental breakfast.
Activities: So far everywhere we have been has touted an large variety of activities.  We could take Moab Utah for example, but really, you will find this anywhere.  You can fill your time with the most expensive forms of entertainment paying out big bucks for jeep rides, hot air balloons, and an endless list of $12 a person museums.  It is sometimes so hard to choose since unless you just fell into some kind of lottery winnings, inheritance, or you are Bill Gates, you aren’t going to be able to do everything that piques your interest.  We have picked three favorite activities which are most often free.  They are: touring the Capitol buildings of the states we visit, hiking, and visiting national parks and monuments. (this one is not truly free but with the America the Beautiful pass that we were given by the Silverton FBC as a going away gift, they are free to us.  The pass is about $80-$85 a year.) We save the activities that cost money for a special occasion.  We plan ahead for them, and look for coupons online that help with the cost.  It also puts it in a different perspective if you think, it will cost our family $50 to do this activity.  We would think nothing about paying that much for a dinner out, so let’s not go out and do this activity instead.  Knowing that we can’t do everything allows us to do our research and narrow the list down to the activities that are truly worth the time and money.  Things like zoos and amusement parks are mostly all the same, we want do the things that are unique and only experienced at this location.
Entertaining the kids in the car: we want the kids to be looking out the windows a lot and we also want them to learn how to entertain themselves.  Chad would say that Audible has been a life saver.  We do listen to a lot of audio books. The kids also have their kindles and they read.  Another big entertainer is their notebooks where they draw and write stories.  We watch for cool new license plates, and which house we would want to live in when we grow up.  That is pretty much the extent of it.  The kids would tell you that they like their long car drives because it is uninterrupted reading time that they wouldn’t get at home.  There are times though, when it is particularly scenic that we make them put their books down and look out the windows.