He'd be a hard one to place in the current paradigm. He is probably the closest things to a left-wing textualist, although he believed the Equal Protection Clause to cover only race and alienage. He almost certainly would've voted against the holdings in Roe v. Wade and Obergefell. On the other hand, he definitely would've voted to uphold the ACA in its entirety under the Commerce Clause. He also definitely would not find much in common with the current right-wing of the Court in terms of religion (among other things, he wrote both Everson v. Board of Education and Engel v. Vitale). The current Court seems to want to bring down the "wall of separation between church and state" that was held to exist under Justice Black's ruling.
I pretty much agree with this. Black would have plenty of problems with the current conservative wing. But he'd have plenty of problems with the liberal wing too. The historical record is clear that he was not at all happy with Goldberg and Fortas, who were basically modern day liberals, near the end of his tenure.