Which non-Xian historians give the most credence to the NT's historical accuracy?

I’m a little confused about what you mean by “broadly accurate” here. I wouldn’t call something that says, “on the road to Nazareth he healed a leper” broadly accurate if the true part is that he went to Nazareth.

Moreover, History is more than just names and dates. The Bible gives us a good look into Historical Sociology and Anthropology, giving us glimpses into how people lived 2000 years ago.

Regardless of Jesus of Nazarath being an actual historical personage.

(I always find these discussions odd. We cannot pinpoint the year Eleanor of Aquitaine was born. We don’t know if Mary or Anne Boleyn was older. We don’t know what happened to the Princes in the Tower. There are things in History that you will never have PROOF for, you’ll just have evidence.)

“Quite a bit”?

I think he wrote something like three paragraphs on what the Christians believe - out of his voluminous works.