One of the Greek words in the New Testament which is often translated as 'visit' is illustrated in the following verses:
NKJ Luke 1:68 "Blessed is the Lord God of Israel, For He has visited and redeemed His people,
NKJLuke 1:78 Through the tender mercy of our God, With which the Dayspring from on high has visited us;
NKJLuke 7:16 Then fear came upon all, and they glorified God, saying, "A great prophet has risen up among us"; and, "God has visited His people."
NKJActs 15:14 "Simon has declared how God at the first visited the Gentiles to take out of them a people for His name.
NKJHebrews 2:6 But one testified in a certain place, saying: "What is man that You are mindful of him, Or the son of man that You take care of [visit] him?
Likewise, in the Greek version of the Old Testament, these may be found:
NKJ Genesis 21:1 ¶ And the LORD visited Sarah as He had said, and the LORD did for Sarah as He had spoken. 2 For Sarah conceived and bore Abraham a son in his old age, at the set time of which God had spoken to him.
NKJGenesis 50:24 And Joseph said to his brethren, "I am dying; but God will surely visit you, and bring you out of this land to the land of which He swore to Abraham, to Isaac, and to Jacob."
NKJRuth 1:6 ¶ Then she arose with her daughters-in-law that she might return from the country of Moab, for she had heard in the country of Moab that the LORD had visited His people by giving them bread.
NKJ1 Samuel 2:21 ¶ And the LORD visited Hannah, so that she conceived and bore three sons and two daughters. Meanwhile the child Samuel grew before the LORD.
NKJPsalm 8:4 What is man that You are mindful of him, And the son of man that You visit him?
NKJPsalm 17:3 You have tested my heart; You have visited me in the night; You have tried me and have found nothing; I have purposed that my mouth shall not transgress.
NKJPsalm 59:5 You therefore, O LORD God of hosts, the God of Israel, Awake to punish all the nations; Do not be merciful to any wicked transgressors. Selah
NKJPsalm 65:9 You visit the earth and water it, You greatly enrich it; The river of God is full of water; You provide their grain, For so You have prepared it.
Psalm 80:14-15 14 Return, we beseech You, O God of hosts; Look down from heaven and see, And visit this vine 15 And the vineyard which Your right hand has planted, And the branch that You made strong for Yourself. [referring to the restoration of Israel].
NKJPsalm 89:32 Then I will punish [visit] their transgression with the rod, And their iniquity with stripes.
NKJPsalm 106:4 Remember me, O LORD, with the favor You have toward Your people; Oh, visit me with Your salvation,
NKJZephaniah 2:7 The coast shall be for the remnant of the house of Judah; They shall feed their flocks there; In the houses of Ashkelon they shall lie down at evening. For the LORD their God will intervene for them, And return their captives.
NKJZechariah 10:3 " My anger is kindled against the shepherds, And I will punish the goatherds. For the LORD of hosts will visit His flock, The house of Judah, And will make them as His royal horse in the battle. [same verb stem both places]
NKJMalachi 3:10 Bring all the tithes into the storehouse, That there may be food in My house, And try [test] Me now in this," Says the LORD of hosts, "If I will not open for you the windows of heaven And pour out for you such blessing That there will not be room enough to receive it.
NKJJeremiah 29:10 ¶ For thus says the LORD: After seventy years are completed at Babylon, I will visit you and perform My good word toward you, and cause you to return to this place.
Inspection of verses such as this amplifies the conception that we have (at our level of perception) that God moves around and inspects things. The Greek word often translated "visit" means this. In the Greek version of the Old Testament, the word often just means "count" -- as when Israel was numbered. So, when God "visits" he performs a "tour of inspection." Just as when he visited Abraham just before he went to Sodom and Gomorrah, to "see for himself" what was going on. We see that the "anthropomorphism" of this kind of thing, while it is an anthropomorphism is still reflective of a real phenomenon in the spiritual world. The omnipresent God, who is not absent at any place in his creation (or elsewhere), is nevertheless specially present at places and times of particular interest to him, at which points he issues blessings, and judgments.
We ought to find Scripture indications of his presence especially at worship.