Welcome aboard the RoadTrip America Forums!
There are two components to any RoadTrip, and they are not somewhat separate. The first is the fuel cost, and that is determined by the miles driven, the efficiency of your vehicle and the cost of gas. We generally recommend that you add about 20% to the miles that mapping software gives you for point-to-point distances to account for 'sidequests', and that you overestimate the cost of gas since it is so prone to significant fluctuations currently. But with that information you can use the Fuel Cost Calculator to get a handle on a gas budget. The other component is food and lodging, and that depends more on the number of days spent on the road than on the miles driven. For this, our recommendation is to assume costs of about $100/day. Yes you can do better on both counts, but consistently skimping on these components, or relying on the kindness of others, can quickly take the joy out of your travels. Hope that gives you an idea of what you'll need to put aside.
AZBuck