Everyone seems to have runout tolerances that they load to, so my question is, what is the best or most common location to take runout readings on loaded cartridges using a sinclair style concentricity guage? Case neck, bullet bearing surface, or some where between bullet bearing surface and bullet tip?

I measure at or near the ogive, as identified by a bullet comparator.

Definitely not on the neck. Neck runout and bullet runout are two different things.

I've always measured the bullet just ahead of the case mouth.

The idea is to measure the most runout, while still getting highly repeatable results. For me, that's measuring in the upper third of the bearing surface.

I measure out towards the tip of the bullet. I know it gives me an exaggerated measurement and therefore if I'm under .003 I'm pretty darn happy. .004 or more and I get it corrected in my tru tool.

I measure the bullet on the bearing surface as far forward as practical. A lot of the slippery bullets don't have that much, so in that case I do it just forward of the case mouth.

I just loaded some 7mag rounds.Nine of each Remington and Winchester brass.First ones were loaded with 160gr Nosler Accubonds.Eight of the Remington cases had .001 or less,one has .004 run out.The Winchesters didn't fare as well.Only two had .002 or less,seven had .003-.005.,one had .009 run out.Then I loaded nine of each with 150gr Nosler CT Silver Tips.This time three of the Remington cases were .002 or less,six were .004-.005.The Winchester cases had four that were .002 or less and five were .003-.004 and one was .007.

I hope you've forgotten to insert some zeros in there.

Fixed it!