Q:

Why did early Christians in Acts still go to the Jewish temple every day?

In the Acts of the Apostles we find that the early believers were every day visiting the temple and afterwards meeting in each others homes.

Every day they continued to meet together in the temple courts. They broke bread in their homes and ate together with glad and sincere hearts, praising God and enjoying the favor of all the people. And the Lord added to their number daily those who were being saved. (Acts 2:46-47, NIV)

If the Old ceremonial ways of the Old Testament were finished at the death of Christ (or as other conjecture after Pentecost) why did the church still attend temple gatherings?  Was it because they were not fully aware of the full implication of the New Covenant and may have even offered sacrifices? Was it because they just wanted to get together and evangelize their brethren? Was it some mishmash of both reasons plus possibly more?  What was going on in their heads?

A:

In Acts 2:1, it is written,

And when the day of Pentecost was fully come, they were all together with one accord (ὁμοθυμαδὸν).
καὶ ἐν τῷ συμπληροῦσθαι τὴν ἡμέραν τῆς πεντηκοστῆς ἦσαν ἅπαντες ὁμοθυμαδὸν ἐπὶ τὸ αὐτό

We see that the first Christians were all together with one accord in the Temple at the time they received the Holy Spirit (Acts 2:4). 
Being Pentecost, "there were, dwelling at Jerusalem, Jews, devout men, out of every nation under heaven" (Acts 2:5), for Pentecost was one of three annual feasts during which men were required to pilgrimmage to the Temple in Jerusalem in order to appear before YHVH (Exo. 23:14-17).
The apostles desired to share the Gospel of Jesus Christ with their brothers (cp. Acts 2:14-41).
And, in Acts 2:46, it is written,

And they, continuing daily with one accord (ὁμοθυμαδὸν) in the Temple, and breaking bread from house to house, ate their food with gladness and simplicity of heart.

So, they continued to remain in the Temple, not all day, but rather, during the morning and evening prayers (our 9 a.m. and 3 p.m.) where a gathering of Jews would always be. This crowd may not have been as large as the one at Pentecost (which only lasted one day), but the apostles took advantage of any opportunity to share the Gospel with as many of their brothers as possible. We even see this with Paul who would rush to Jerusalem for a feast in order to share the Gospel (cp. Acts 18:21).

A:

The simple answer is that in the very early days the followers of Jesus considered themselves to be Jews. They saw Jesus as the fulfilment of the Jewish laws and prophecies - that he had come to redeem Judaism and the Jews, not to set up another religion. The idea that Gentiles might be followers of Jesus without also becoming Jews would only be controversially considered many years later.
Therefore it is entirely natural that they would continue to meet in the Temple.  They were also following Jesus' example, who had taught crowds in the Temple only a few months before. The Temple was much more than just the place of sacrifice - it was the central point of the Jewish religion, and the place to go to spread the word to other Jews.

