I think part of the reason why I have an odd interest in the [bones of St Cuthbert] (https://en.wikipedia.org/wiki/St_Cuthbert%27s_coffin) (is it actually him in there? did they switch the body out in the 1500s?) is the sheer fascination that here we have the remains of a known person from way back in the 600s, that we know many other things about from documentary sources (Uhh, assuming it's him in there). There are not a lot of historical figures that old, about whom we can say we know where they're buried.
Most tombs that old are empty by now, and the human remains we find from back then are anonymous. Except for Cuthbert. Is there anyone older still?
Tomb of Confucius (479 BC) is the oldest I can think of off the top of my head. Qin Shi Huang (210) is quite well known because its quite posible it originaly contained rather a lot of mercury. In general I suspect you are going to be looking at far eastern graves. Anything else doesn't has records that far back or has suffered serious damage from war, grave robbers or collectors.