Accuracy International, Steyr, and Tikka.
But I guess Accuracy International is a given.
Steyr.
I know they are a little more than the average rifle, but they have never disappointed. In order, I’ve had an SSG-69 P-I, Scout .308, AUG A3, SSG-69 P-II, and a SafeBolt SBS in .300 Win Mag. They’ve all shot better than they should have.
The accuracy of the Steyr SSGs is pretty well known. I was using my second one at LR matches at Atterbury (800-1000) until I got my AI. All factory. The barrel on those is none too hefty by today’s standards.
The Scout’s barrel is really light. Really super light, plus it’s fluted in addition. Yet it shoots well, even when warm/hot. Best of all to me is that almost everything shoots to the same zero at 100 yards.
The Steyr AUG isn’t known as a target rifle, and the factory barrel in mine was nothing exciting but it did OK. Like the Scout, heating had little to no effect. I’ve since bought a factory 20” 1/7 twist (original is 16” 1/9) and that barrel shoots really well.
The SBS .300 Win Mag is a treat. It’s a fairly light rifle for the caliber, but it hovers juuuust above .5 MOA, although the farthest I’ve put it on paper was 240 yards.
My buddy bought one in .30-06 that does the same.
Granted, a Steyr costs more than a Savage Axis, but they might not be as crazy as you think. There are several on Gunbroker right now from 500 to 700. Compared to what current new Ruger Americans are running, they aren’t that far off.
A lot of people buy Savages to replace the barrel, then the cost gets well beyond a regular Steyr hunting rifle.
Tikka
While I don’t own any, I’ve seen quite a few Tikkas, and they all shoot really well. My buddy who bought the .30-06 Steyr has three Tikkas now, I think, and he doesn’t keep rifles that don’t shoot. Their price is starting to match their reputation now, but they are still about as close to a sure thing I know of.