Where God is worshipped is now irrelevant, as the Lord Jesus himself taught. It is not where, but how we worship Him that is important. Because God is a Spirit and He is to be found everywhere, we don't have to go to a special place or building. True worshippers worship Him in spirit and in truth (John 4:21-24).
In olden times it pleased God through His servant Moses to instruct His people, Israel, to build Him a tabernacle, a portable temple or sanctuary, that He might dwell among them (Exodus 25:8). The ark was God's throne and it was the first article of furniture that they were to build. The Lord took the place of a king in a theocratic nation.
Centuries later, king David at the end of his life instructed his son, Solomon, and the leaders of Israel, to build a "house" for the name of the Lord, to be His sanctuary (1 Chronicles 22:19). King Solomon built a sumptuously decorated temple in Jerusalem, according to plans laid down by his father. But at its dedication, he wisely proclaimed "But will God indeed dwell on the earth? Behold, heaven and the heaven of heavens cannot contain You. How much less this temple which I have built!" (1 Kings 8:27).
Any idea that God dwells in a physical building is a totally false pagan notion. There is no such thing as "God's house" because He cannot be confined within a building made by the hands of men. It is never implied that God would be restricted to a geographical spot for the purpose of being worshipped. When it is said that He dwelt between the cherubim over the ark in the "holy of holies" it means that His presence with the people of Israel was physically represented over the "mercy seat" between the two golden cherubim attached to it (1 Samuel 4:4; 2 Samuel 6:2; 2 Kings 19:15 and Isaiah 37:16). All objects and ceremonies within the tabernacle and temple had a spiritual meaning and pointed to the Messiah Jesus. Since He came and gave His blood in propitiation for the sins of men, they have been fulfilled and the symbols are no longer required.
Instead of a temple made of stones by the hands of men, God is now building Himself a spiritual temple where His Spirit dwells, which is the church of Christ (Ephesians 2:20-21), the cornerstone of which is Christ, the foundations are the apostles and each stone is a believer. A local assembly will be "the house of God, which is the church of the living God, the pillar and ground of the truth" if it is submissive, faithful and obedient to Him. It is essential for the practice of love and fellowship between believers, instruction, mutual support, and growth "into a holy temple in the Lord, built together for a dwelling place of God in the Spirit." (Ephesians 2:21-22). Every believer is also a temple of the Holy Spirit (1 Corinthians 6:19).
The Lord Jesus promised his disciples "where two or three are gathered together in My name, I am there in the midst of them." (Matthew 18:20). It is not required to be in a temple, or in a house, the gathering can even be in the open air. The only essentials are that the gatherings are made in the name of the Lord Jesus, implying that those involved are His servants and that what they are doing is on His behalf, and that they worship in spirit and in truth. This is what matters, not where, but how: in the spirit of man, according to the Holy Spirit (Romans 8:5) who is the Spirit of truth (John 16:13).
As to the communion of the Lord's Supper, much has been written, many different practices have arisen and much dissent has resulted from this practice which was ordained by our Lord Jesus. What was meant to be a symbol of the Lord himself, taking human form and giving his body and blood for our redemption on the cross, and in that way uniting believers in redemption under His lordship, has been used for fetish worship, division, segregation and exclusivity, for the shame of the name of Christ. There is no room here to investigate and discuss the reasons for all the different practices, but we shall only verify what concerns the question: the place where it ought to be held.
We have very few examples from the early church:
The first Lord's Supper was instituted by the Lord himself, in the presence of His apostles, after they had all sat down and eaten the Passover meal in the guest chamber of a house.
The next time we read about the Lord's Supper is in a letter by the apostle Paul to the Corinthians: the church assembled together in one place for a meal, at which they held the Lord's Supper (1 Corinthians 11:13-24). Paul declares that the selfish and disrespectful conduct of some of the participants made it impossible to regard it as the Lord's Supper at all. The place, or places, where the church met isn't mentioned anywhere - it seems to have been irrelevant.
There are a few instances where eating a meal, usually called "breaking of bread", probably also involved the Lord's Supper, although this is not clearly stated. In Acts 2:46, for example, we read that the early church continued daily in the temple and broke bread from house to house; in Troas the disciples during their travel came together in the upper room of a house to break bread … and Paul broke bread and eat, and talked a long while (Acts 20:7-11). In Vine's opinion "As to whether Acts 20:11 refers to the Lord's Supper or to an ordinary meal, the addition of the words 'and eaten' is perhaps a sufficient indication that the latter is referred to here, whereas verse 7, where the single phrase 'to break bread' is used, refers to the Lord's Supper. A parallel instance is found in Acts 2:42, 46. In the former verse the phrase 'the breaking of bread,' unaccompanied by any word about taking food, clearly stands for the Lord's Supper; whereas in verse 46 the phrase 'breaking bread at home' is immediately explained by 'they did take their food,' indicating their ordinary meals."
The impression is left that the Lord's Supper was, at least at first, a part of a joint meal of the Christian community. Later, as instructed in the letter to the Corinthians, believers were to eat their meals at home and only partake of the symbols, bread and cup, when they met. The Lord's Supper was instituted for the specific purpose of remembering the Lord Jesus and announcing his death and resurrection until he comes for His church. This leads us to worship God and His Son for the righteousness, mercy and love shown towards us, sinners. The place for meeting for this purpose, day of the week and time are left entirely at the discretion of those participating.