Theism (the 3-O God) is the definition most often associated with the arguments for God's existence in Ancient and Medieval Philosophy.
One will often hear the property of 'omnipresence' attributed to God under Theism, although this should be resisted for two reasons. First, omnipresence is probably meant by most theists to just mean omniscience; i.e., if God knows all that can be know, God must be everywhere to know what can be know. But of course it is not necessary for a being to be present at an event in order to have knowledge of the event. Second, and more problematically, according to Theism, God is supposed to be distinct from the Universe in that he does not have spacio-temporal properties. However, 'presence', even 'omnipresence' is a spacio-temporal property. Hence, 'where-ness' is not a property appropriately attributed to the God of Theism. Though it sounds paradoxical, it would be more appropriate to say that God is 'nowhere' rather than 'everywhere'.
Omnipresence would be an appropriate property of God on the pantheistic definition since God and the Universe are identical—whereness is a property of the Universe, so God will necessarily have that property.