About 250 miles at the minimum. RVs with smaller gas tanks have good mileage, RVs with lower mileage usually have higher gas capacity. You should get about 250+ miles on a full gas tank. If you run the generator while RV is moving then this will be lower depending on how long you run the generator for.
If you plan well then travelling cross country on a rental RV should not be an issue from gas station point of view.