How do I keep LEGO boxes looking their best for as long as possible?
While the LEGO plastic elements are very durable and should be considered as safe as long as they remain in their box, the boxes themselves are much more vulnerable.

As you mention, direct sunlight may be damaging to the printing, but you'll also need to be wary of humidity and possible shocks.

As a minimum, I'd recommend storing them in another cardboard box, if possible an original one from LEGO as dimensions will match better. If not, you'll need to make sure there is sufficient padding so that your LEGO box doesn't move freely in the cardboard box. Padding might be a good idea anyway if you aren't too sure of how careful you'll be with the outer box, a dented corner happens very fast.

Of course, you'll want to store the boxes in a dry area, and out of reach of other hazardous elements (cats come to mind - shredding boxes is the raison d'être of some, the rest prefer peeing on everything which you'll want to avoid too).

All this isn't exactly specific to LEGO, but my last bit of advice would be to turn the boxes from time to time so that the weight of the elements settling inside don't always affect the same side. Or at the very least, store your boxes flat. If you were to store a big box on the same side, the bricks inside will put enough pressure on the side that they'll eventually deform them.