Quanta Magazine does an excellent job with balancing accessible writing and advanced topics. It's just enough to get someone interested in the problem and the basic ideas to start thinking about it.
Granted, I'm not sure how common this is.
I do worry about Gell-Mann amnesia with Quanta, but I comfort myself that usually nobody has a stake in distorting this or that number theory thingamajig or physics quandary. However... I'm sure there are academic infights and research tug-of-war to which I'm blissfully blind.