Bring your own water bottles and fill up at water fountains and at the hotel, to make sure you don't get thirsty and have to buy one at a gas station.
Definitely bring a cooler. I've found that the collapsible ones are particularly useful for road trips.
I've also heard-but haven't tried it myself-that slow cookers are really useful when you want to avoid eating out but aren't staying in the same place each night. There are just so many things you can use them for- warm breakfasts in the mornings, many different recipes for lunch and dinner, and virtually no other cooking utensils required.
Bring "emergency" food. For that moment when you are hangry and would otherwise succumb to the gas station candy aisle. Tasty cashews and fruit usually works best for me.
I've also found that bringing food storage and utensils (forks, spoons, etc.) help me take advantage of hotel/Airbnb freebies and grocery-store food. That way you won't be trying to lick the yogurt out of the carton. I usually bring both plastic bags and a few tupperware, because then you can put anything that is fragile (nectarines, grapes, etc.) in the tupperware without fear of it being crushed by the 6 pack in the cooler :).
Ask your hosts what activities are free in the are you are staying. They will likely have some awesome ideas.
Also ask your hosts where to buy cheap groceries locally.
Depending on your route and your plans you may also want to buy a National Parks pass. That way you have just one upfront fee instead of multiple daily fees.
Make sure to bring appropriate weather gear, so you don't have to buy expensive gas-station umbrellas/ponchos at the last minute.
Think about a thoughtful but cheap gift for the aunt and uncle to thank them for letting you stay with them. For example, many people will appreciate if you make them a delicious home-cooked meal with some special treats (like local beer from your hometown and something they really like for dessert) even more than they would like a fancy night out at a restaurant.