closeness has 13 distinct synonyms spread across 6 of its 6 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is openness.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
a feeling of being intimate and belonging together
“their closeness grew as the night wore on”
extreme stinginess
characterized by a lack of openness (especially about one's actions or purposes)
close or warm friendship
“the absence of fences created a mysterious intimacy in which no one knew privacy”
Synonyms, antonyms and the broader and narrower relations for closeness come from Princeton University’s WordNet. Full sources and licences.