The book of Hebrews is, among other things, a witness to the historical Jesus. As such, dating the book early can suggest it has more value as a historical witness than dating it later.
Mind you, I don't think that's intrinsically significant. A second generation Christian could live well past 70 AD. And, in any event, Hebrews is inspired.
Nevertheless, in terms of Christian apologetics, it's worth considering the date–since we're not necessarily dealing with believers.
Some scholars think the reference to Timothy in 13:23 means Paul was still alive, although their inference is unclear to me.
The best argument for a pre-70 date is the author's silence on the destruction of the temple. If the book was written after 70 AD, surely he'd use the destruction of the temple to illustrate his point.
In objection it is said that his argument is structured around the tabernacle rather than the temple. However, that objection is circular:
i) His argument may be structured around the tabernacle in large part because the temple was still standing, so he couldn't use that to make his point. Had it been destroyed by then, it would make sense to use it.
ii) In addition, the tabernacle was inherently temporary, so that was a natural illustration.
There is, however, a neglected argument for the pre-70 date. Scholars typically think what occasioned the book was a church in crisis. Some think it was addressed to a house-church in Rome.
More generally, they think it was addressed to a Messianic congregation, or at least a church with significant Jewish-Christian representation. Members were tempted to commit apostasy by reverting to Judaism because Christians were facing persecution from the Roman authorities, and Judaism was a religio licta. They figured they could enjoy the political and religious advantages of Judaism without the disadvantages of Christianity.
If, however, Hebrews was written after 70 AD, it's hard to see how that would remain an attractive option. Some Roman authorities always viewed Jews as troublemakers. And surely the Jewish revolt hardened Roman attitudes towards the Jews. So it's unclear how reverting to Judaism would afford them special protection, considering the official and unofficial hostility that would be directed at Jews on the heels of the Jewish revolt. And that consideration is intensified in this congregation was located in the capital city of the Roman Empire.
If, however, the temple had been destroyed, then there's a sense in which they couldn't go back. To be sure, the Babylonian exile might furnish a precedent, but that's an inauspicious precedent.