I agree with Jay, finding areas of zero noise are to be cherished and milked for all they're worth. In my experience, even being 50+ miles away from Los Angeles in the Carrizo Plain, my recording rig still picked up LAX air traffic to a high enough level that we had to wait for planes to clear. It's very unfortunate the degree of oblivious noise pollution in our world.
That said though, I suggest digging deep into the recordings and maybe even make some wind!
I've done some recording out in the Mojave desert wherein there were large areas of dead silence (thankfully), and seemingly dead air in a canyon with no movement. Yet, in the studio I cranked the dead air and played with some EQ, which resulted in discovering some interesting gentle wind tones which do have some subtle movement to them, yet have the weight and presence of a pleasantly round wind. Admittedly, they're some of my favorite go-to winds when I'm in the edit.
You may be quite surprised at what you'll find buried in quiet recordings.
I highly agree with the other comments of sunrise/sunset recordings. Some of the best opportunities I have found have been when I jet out to nature at about 6:00 AM when the birds are waking at first light. Usually by about 9:00 AM the birdsong has all but tapered off. Speak with rangers or guides about what you're seeking, they tend to be very enthusiastic and helpful, and not only provide you a list of local birds and info about them, but they may even be able to pinpoint great spots on a map where particular birds nets or hang out.
In very remote areas, especially deserts, my experience has been that there's a lot of sitting and waiting involved - in the sense that you may be recording a whole of nothing until something really cool crosses your path in the blink of an eye.