To pay a visit is to go and see somebody for a while. Coat on, a tin of biscuits under your arm, an hour in a warm front room.
The money metaphor once more, and here it makes the whole thing sound like a small duty discharged, which is exactly the tone. It takes to. Compare visit her, which is neutral, with pay her a visit, which in the wrong mouth turns faintly menacing — that is how people in films describe going round to have a word.
1phrasepay a visitTo go and see somebody for a while.
“We will pay a visit to your aunt on Sunday.”
pay a visit is a short social call.
Practised in Common Word Pairs