I don't know of many magazines that are published for general reading by Christian organisations; the ones I do know of are for Christian consumption (and not always helpful in that regard, I might add: I think of Southern Cross, the Anglican tabloid), New Life, a more generally marketed paper, the self-consciously pretentious Eternity put out by the Bible Society; but that's about all. There used to be On Being, later called Alive, I think, and then a purely e-publication now seemingly disappeared, perhaps due to its drift to irrelevancy. For those who liked controversy, there was Robert Brinsmead's Verdict (I'm harking back to the early 1980s, and no, I have no SDA connection), and any number of US and UK publications.
However, these were or are all very internal, not for the general reader, and of no interest to the non-Christian, yet, here is an opportunity; print media still works, you can leave it around, put it in waiting rooms, and so on.
At a visit to the local SDA hospital with a relative recently, I picked up a copy of Signs of the Times. This fits the bill. It doesn't always hit my buttons, but for general interest and popularised Christian themes (even soft-peddling the SDA bit) it works. I read it from cover to cover and it was upbeat, practical and helpful. No offensive new age like twaddle, just straight talk for grown ups.