What's the best way to run big tires and still maintain good fuel mileage? I consider good mileage 15 mpg at minimum, but ideally 20 mpg is better.
The short answer is don't install big tires if fuel mileage is your primary concern. Anybody that has gone from stock-sized tires to 37s with no other changes and claims little if any fuel impact is either lying or needs a lesson on how to track mileage.
Fact: Big tires make mileage go down. Are there things you can do to recover much of the mileage that has been lost due to installing larger tires? Yes, absolutely. Changing axle gear ratios to compensate for the taller tires is the primary and best way to restore most of the mileage you lose when going with bigger tires. Changing axle gears to lower (numerically higher) gears places the engine back in its optimum powerband and puts the transmission shift points back where they are supposed to be without the need for special programmers. That said, many newer vehicles require a programmer to adjust the PCM to recognize the new gear ratio without freaking out. Such is the modern age we live in.
But notice we said changing axle gears can get back most, not all the mileage you lose. A larger tire and wheel package is much heavier than the stock package, and the increased weight means more rolling resistance. Greater rolling resistance means more drag, and more drag means a dip in mileage. With all the fuel economy regulations the OEMs face these days, you can bet that if there were a way to improve mileage by installing 38s or 40s, the OEMs would have done it.
Changing axle gears requires a substantial investment, just like the larger tire and wheel package as well as the lift you invested in to clear those bigger tires. Depending on how you drive and where you live, you may be able to recoup that investment over time with the improved mileage. That said, you'll likely never recoup the investment over the life of the vehicle, especially when comparing the cost of replacement large tires to that of stock replacements.
If you're trying to make a logical case for big tires on anything other than a dedicated off-road vehicle, save yourself the hassle. You'll never be able to justify bigger tires on paper compared to stock tires, whether it's mileage, wear and tear, or even on-road vehicle performance. That's not the point. The point is enhancing your vehicle's off-road performance and customizing your vehicle so that it looks cool to you and different from the thousands of carbon copies of your vehicle. Bigger tires deliver better off-road performance in spades, which is what most of us prioritize over optimum mileage.