I could produce more quotes, but let's start with these two sources for now. The first author is semi-longish, which is one reason I decided to limit the quotations.
From Louis Berkhof:
The infinity of God may also be viewed with reference to space, and is then called His immensity. It may be defined as that perfection of the Divine Being by which He transcends all spatial limitations, and yet is present in every point of space with His whole Being. It has a negative and a positive side, denying all limitations of space to the Divine Being, and asserting that God is above space and fills every part of it with His whole Being. The last words are added, in order to ward off the idea that God is diffused through space, so that one part of His Being is present in one place, and another part in some other place. We distinguish three modes of presence in space. Bodies are in space circumscriptively, because they are bounded by it; finite spirits are in space definitively, since they are not everywhere, but only in a certain definite place; and in distinction from both of these God is in space repletively, because He fills all space. He is not absent from any part of it, nor more present in one part than in another.
In a certain sense the terms “immensity” and “omnipresence,” as applied to God, denote the same thing, and can therefore be regarded as synonymous. Yet there is a point of difference that should be carefully noted. “Immensity” points to the fact that God transcends all space and is not subject to its limitations, while “omnipresence” denotes that He nevertheless fills every part of space with His entire Being. The former emphasizes the transcendence, and the latter, the immanence of God. God is immanent in all His creatures, in His entire creation, but is in no way bounded by it. In connection with God’s relation to the world we must avoid, on the one hand, the error of Pantheism, so characteristic of a great deal of present day thinking, with its denial of the transcendence of God and its assumption that the Being of God is really the substance of all things; and, on the other hand, the Deistic conception that God is indeed present in creation per potentiam (with His power), but not per essentiam et naturam (with His very Being and nature), and acts upon the world from a distance. Though God is distinct from the world and may not be identified with it, He is yet present in every part of His creation, not only per potentiam, but also per essentiam. This does not mean, however, that He is equally present and present in the same sense in all His creatures. The nature of His indwelling is in harmony with that of His creatures. He does not dwell on earth as He does in heaven, in animals as He does in man, in the inorganic as He does in the organic creation, in the wicked as He does in the pious, nor in the Church as He does in Christ. There is an endless variety in the manner in which He is immanent in His creatures, and in the measure in which they reveal God to those who have eyes to see. The omnipresence of God is clearly revealed in Scripture. Heaven and earth cannot contain Him, I Kings 8:27; Isa. 66:1; Acts 7:48,49; and at the same time He fills both and is a God at hand, Ps. 139:7-10; Jer. 23:23,24; Acts 17:27,28.
International Standard Bible Encyclopedia:
Neither the noun "omnipresence" nor adjective "omnipresent" occurs in Scripture, but the idea that God is everywhere present is throughout presupposed and sometimes explicitly formulated. God's omnipresence is closely related to His omnipotence and omniscience:
that He is everywhere enables Him to act everywhere and to know all things, and, conversely, through omnipotent action and omniscient knowledge He has access to all places and all secrets (compare Psalms 139). Thus conceived, the attribute is but the correlate of the monotheistic conception of God as the Infinite Creator, Preserver and Governor of the universe, immanent in His works as well as transcendent above them.