Theists often tick off certain properties that purportedly identify God as the maximal being or greatest possible being, etc. As one of Jehovah's Witnesses, I have been taught that God is omnipotent (almighty), omniscient (all-knowing), infinite (though we have to carefully define that term), and he is all-wise and is love (1 John 4:8).
Other properties could be added to the list, but it is common to say that God has all omni-properties and that such properties are compossible, which means that said properties jointly exist. Moreover, if God has one omni-property, then God has all. Otherwise, God (Jehovah) would not be God--the maximal being, who possesses all great-making or deific properties.
While most of the omni-properties don't seem problematic from a Witnesses standpoint, I always have to remember that we do not believe omnipresence is a divine property. Jehovah's Witnesses believe that Jehovah God resides in one location (as it were)--namely, heaven itself (1 Kings 8:27, 30, 32, 36, 43, 45, 49). By "heaven," I am referring to a realm that apparently transcends the physical spacetime universe: Paul spoke of the third heaven in 2 Cor. 12:2. Although he dwells in heaven along with spirit creatures known as angels, his power and spirit are manifested everywhere.
So is God omnipresent? Does he have all omni-properties? So far, it seems that omnipresence is a divine property, yet God is still God.