The idea that someone would suggest the Spectator—more reactionary troll factory than magazine at this point—as a response to someone who feels the NYT is pushing too much of an agenda is absolutely hilarious.
My complaint about the NYT and many other news sources is absurd combination of a hyper-specific and rapidly-changing set of beliefs, along with brutal enforcement of those beliefs.
My challenge to you: write down your beliefs on a controverial topic (on paper). Wait 6 months and pick up the NYT. My prediction: they will be in the process of canceling someone for those same beliefs, and you will shred the piece of paper out of fear.
OK, maybe that's an exaggeration. But I wouldn't be shocked if it was too close for comfort.
It's definitely right-of-center and doesn't mind cocking a snook at left-wing holy cows, but it's not a "reactionary troll factory".
I haven't said the Guardian or NYT is better.
It's not "disagreement" -- they regularly publish easily checkable objectively false information.
Magazines publishing centre-right views are fine. But if what you are seeking is a news publication that doesn't push a particular agenda, then The Spectator is pretty much as far away from it as you can get outside of Pravda.
You're right, of course, that it publishes some mild centre-right commentators with uncontroversial conservative views. That doesn't really compensate, in my view, for the provision of space to writers like Liddle and Young. These particular people are reactionary trolls; their writing contains little other than disinformation deliberately intended to stoke culture-war nonsense, and they're too smart to believe what they write. This stuff does little more than make society worse for everyone.
But I'd say regardless of your views on individual commentators or the overall quality of the publication – if someone wants to avoid the NYT because it is campaigning too much, then directing them to The Spectator is laughable.