Do I have to give my lay by him in store to my local congregation "upon the first day of the week" or could I give it to the congregation that I am visiting on that particular Sunday?
Second Corinthians 9:7 says, "Every man according as he purposeth in his heart, so let him give; not grudgingly, or of necessity: for God loveth a cheerful giver." From that verse we learn that we must give, that we must give as we have purposed in our hearts, and that our giving must not be done grudgingly or of necessity. But to whom should we give? That is really the question you are asking.
For many and perhaps most Christians, giving occurs once a week and the gift is presented to the elders of the local congregation for their use in the kingdom of God. And there is nothing wrong, and in fact very much that is right, with that model of giving. But, there is nothing at all that prevents you from also giving directly (rather than through your local eldership) to other congregations or other works of the church (such as missionaries or children's homes).
To address your question directly, there would be nothing wrong per se in giving to the congregation you are visiting on the day that you are there rather than to the local congregation on the day you are not there. But, that action could be wrong if you have committed to give a certain amount to the local work or if your local congregation has been given cause to believe that you will give a regular amount and has acted in reliance on that belief. Remember, we are to give as we have purposed, which suggests our giving should not be haphazard, which would be the case if our gift could not be relied upon.
Perhaps the best option when visiting a congregation is to give to the work there and then also to make up your gift to your local congregation when you get back home. But give you must, even when on vacation. Some Christians take summer vacations and do not give at all during that time, which means they are asking God to pay for their vacation!
A final note, sadly, is that for some local congregations those who are called elders cannot be trusted to faithfully handle the gifts with which they are entrusted. When that happens, you should leave if possible. If you must remain, my suggestion is that you send your entire gift or at least a large portion of your gift to a children's home or a faithful congregation where you know it will be put to good use. The elders have a tremendous responsibility to faithfully handle your gift -- but your responsibility does not end when you drop the gift in the collection plate! If you know your gift is not being put to good use, then you must give elsewhere. After all, how can it be said that you are giving to God when you know the money is going elsewhere?
You Must Hear the Gospel
Romans 10:17
You must hear the gospel and then understand and recognize that you are lost without Jesus Christ no matter who you are and no matter what your background is. The Bible tells us that “all have sinned, and come short of the glory of God.” (Romans 3:23) Before you can be saved, you must understand that you are lost and that the only way to be saved is by obedience to the gospel of Jesus Christ. (2 Thessalonians 1:8) Jesus said, “I am the way, the truth, and the life: no man cometh unto the Father, but by me.” (John 14:6) “Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved.” (Acts 4:12) "So then faith cometh by hearing, and hearing by the word of God." (Romans 10:17)
You Must Believe
Hebrews 11:6
You must believe and have faith in God because “without faith it is impossible to please him: for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him.” (Hebrews 11:6) But neither belief alone nor faith alone is sufficient to save. (James 2:19; James 2:24; Matthew 7:21)
You Must Repent
Acts 3:19
You must repent of your sins. (Acts 3:19) But repentance alone is not enough. The so-called “Sinner’s Prayer” that you hear so much about today from denominational preachers does not appear anywhere in the Bible. Indeed, nowhere in the Bible was anyone ever told to pray the “Sinner’s Prayer” to be saved. By contrast, there are numerous examples showing that prayer alone does not save. Saul, for example, prayed following his meeting with Jesus on the road to Damascus (Acts 9:11), but Saul was still in his sins when Ananias met him three days later (Acts 22:16). Cornelius prayed to God always, and yet there was something else he needed to do to be saved (Acts 10:2, 6, 33, 48). If prayer alone did not save Saul or Cornelius, prayer alone will not save you. You must obey the gospel. (2 Thess. 1:8)
You Must Confess
Romans 10:9
You must confess that Jesus Christ is the Son of God. (Romans 10:9-10) Note that you do NOT need to make Jesus “Lord of your life.” Why? Because Jesus is already Lord of your life whether or not you have obeyed his gospel. Indeed, we obey him, not to make him Lord, but because he already is Lord. (Acts 2:36) Also, no one in the Bible was ever told to just “accept Jesus as your personal savior.” We must confess that Jesus is the Son of God, but, as with faith and repentance, confession alone does not save. (Matthew 7:21)
You Must Be Baptized
Acts 2:38
Having believed, repented, and confessed that Jesus is the Son of God, you must be baptized for the remission of your sins. (Acts 2:38) It is at this point (and not before) that your sins are forgiven. (Acts 22:16) It is impossible to proclaim the gospel of Jesus Christ without teaching the absolute necessity of baptism for salvation. (Acts 8:35-36; Romans 6:3-4; 1 Peter 3:21) Anyone who responds to the question in Acts 2:37 with an answer that contradicts Acts 2:38 is NOT proclaiming the gospel of Jesus Christ!
You Must Be Faithful Unto Death
Revelation 2:10
Once you are saved, God adds you to his church and writes your name in the Book of Life. (Acts 2:47; Philippians 4:3) To continue in God’s grace, you must continue to serve God faithfully until death. Unless they remain faithful, those who are in God’s grace will fall from grace, and those whose names are in the Book of Life will have their names blotted out of that book. (Revelation 2:10; Revelation 3:5; Galatians 5:4)