visit has 22 distinct synonyms spread across 7 of its 13 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. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
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.
impose something unpleasant
“The principal visited his rage on the students”
talk socially without exchanging too much information
“the men were sitting in the cafe and shooting the breeze”
stay with as a guest
“Every summer, we visited our relatives in the country for a month”
assail
“He was visited with a terrible illness that killed him quickly”
the act of going to see some person or place or thing for a short time
“he dropped by for a visit”
a meeting arranged by the visitor to see someone (such as a doctor or lawyer) for treatment or advice
“he scheduled a visit to the dentist”
the act of visiting in an official capacity (as for an inspection)
Synonyms, antonyms and the broader and narrower relations for visit come from Princeton University’s WordNet. Full sources and licences.