Hebrews is an enigmatic book. We don’t know who wrote it, we don’t know who it was sent to. It’s subject matter is rather different than the other letters in the New Testament, though entirely consistent with them. For most people there are individual verses of Hebrews that they are familiar with, such as Heb 4:12; 4:15,16; 6:19, along with the famous chapter 11 on the heroes of faith, and chapter 12 on God disciplining His children. Then there is the section in this enigmatic book on that enigmatic character Melchizedek, and the main focus of the book is on how the old covenant foreshadowed the new, and how the gospel completely supersedes the old covenant. Hebrews helps us understand the Old Testament.
As always, any insight or assistance I might give is built upon the work of many others. My main source will be:
Hebrews - Tyndale New Testament Commentary, D Guthrie (1983)
The reason we don’t know who wrote it nor who it was sent to is that the letter doesn’t tell us. So why is it included in the New Testament? Well it was referred to from very early times, the earliest record being that of Clement of Rome. It was also included in early collections of the New Testament books, and was grouped with Paul’s letters. This is why some think that Paul wrote it, though that view is not held by many these days. The reasons for doubting Pauline authorship are that in his other letters the personal nature of the letter and his authorship are very clear, in Hebrews there is no mention at all. The subject matter and style are very different from (though consistent with) Paul’s letters.
Tertullian contains quotes from “an epistle to the Hebrews under the name of Barnabas”. Martin Luther suggested that Apollos wrote it. The reasoning is that Apollos was an intellectual Jewish Christian, and so would have been capable of writing the letter. There have been various other suggestions as to the authorship. As Origen said “God alone knows the truth of the matter”.
There have been two main suggestions as to the destination, Palestine and Rome. Palestine was proposed because of the emphasis on the Jewish religion in the letter, but the Greek is of a high standard, and there is no mention of the temple. Rome was the first place where the letter is referred to, by Clement. Also it took a long time for the Western church to ascribe the letter to Paul and that may be because in earlier years people knew Paul had not written it. However, Rome is still just a guess. Whatever the case, the readers were probably Jewish Christians, or at least Christians who were questioning how the gospel fitted in with the Old Testament.
The question of the date is somewhat easier to deal with. It is almost certain to have been prior to AD 70 and the destruction of Jerusalem, otherwise there would surely have been mention of this. For the place of the sacrifice is a key theme in Hebrews, and the sacrifices stopped after the destruction of Jerusalem.
The place of Hebrews in the canon of scripture was never in doubt in the eastern church, but it did take longer for it to be fully recognised in the West.