brief, fleeting (esp. BrE), flying (BrE), quick, short
little
I think it's time we paid him a little visit.

extended, lengthy, long
eight-day, hour-long, weekend, etc.
regular
routine
frequent, repeated
She enjoyed the frequent visits of her grandchildren.

infrequent, occasional, periodic, rare
annual, daily, twice-weekly, etc.
repeat
recent
last, previous
forthcoming (esp. BrE), impending, upcoming (AmE)
The President has been briefed in preparation for his forthcoming visit to Russia.

exchange (esp. BrE), reciprocal, return
Exchange visits between company and school have kept the project going.
They came here last week, and we'll pay them a return visit in the summer.

surprise, unannounced, unexpected
planned, scheduled
unwelcome
casual
formal, ministerial (esp. BrE), official, presidential, royal, state
high-profile
family, private, social, unofficial
foreign, overseas (both esp. BrE)
personal
Following her letter of complaint, she received a personal visit from the store manager.

home (BrE)
You should receive a home visit from your midwife within a month.

hospital, prison
dental, doctor's, emergency-room, medical, office (all AmE)
first, initial
follow-up
educational (esp. BrE), study
fact-finding (esp. BrE), research
inspection
on-site, site
campus (AmE), school
memorable

conduct (formal), go on, make, pay sb, take, undertake (formal, esp. BrE)
We used to go on school visits to museums and historical buildings.
How many doctors are still able to make home visits?
Pay us a visit next time you're in town.

get, have, receive
look forward to
I'd been looking forward to my friend's visit for some time.

arrange, organize, plan, schedule
postpone
cancel
cut short
He was forced to cut short a visit to North America.

announce
We received a letter announcing a visit from government inspectors.

be (well) worth
If you're staying in Rome, Ostia is well worth a visit.

during a/the visit, on a/the visit
On one of her regular visits home, she told her parents she was engaged.

visit from
We had a visit from somebody collecting for charity.

visit to
a visit to the dentist

visit with (AmE)
He thought back to his visit with the doctor.

frequently, often, regularly
occasionally, sometimes
rarely
personally
online

come to, go to
My parents are coming to visit me next week.
We've just been to visit my grandparents.

decide to, hope to, intend to, plan to, promise to, want to, wish to
be expected to, be likely to
A million people are expected to visit the museum over the next 12 months.

invite sb to, urge sb to

with
Come and visit with me sometime.

Visit is used with these nouns as the subject:
delegation, inspector, tourist

Visit is used with these nouns as the object:
area, bar, blog, brothel, cathedral, cemetery, clinic, collection, country, destination, exhibition, facility, fair, farm, festival, gallery, grave, homeland, lavatory, library, mall, museum, neighbour, neighbourhood, optometrist, page, park, prostitute, region, relation, relative, restaurant, salon, seaside, shopping centre, showroom, shrine, sick, sight, site, store, theatre, toilet, veterinarian, website, zoo