The honest answer for a wet day here is a short list. Six places are filed under it, and they are good, but this is country for hills and houses, and much of it closes in winter. Choose by how far you are prepared to drive.
Banbury Museum and Gallery is the place to go when it rains. It is free, it has lifts to every floor, and the Waterways Gallery spans the canal. The charged exhibitions in the Pye Gallery are the variable part, so see what is on. Tooley's Boatyard is next door, though the trust opens it only from 10am to 1pm, Tuesday to Saturday, so make it a morning. Lock29 is a few minutes away on Castle Street, with food and drink traders under one roof for lunch. Good Game on the High Street, which calls itself Banbury's first board game café, is the other wet-afternoon answer. Book a table online, and check the hours, which its site does not print.
Worth a drive
Compton Verney is the best choice if the weather has set in for a day. It is a gallery with six permanent collections and changing shows, with lifts to each floor of the galleries, and its own site gives the same Wednesday to Sunday hours with no winter closure. Allow most of the day. Upton House has paintings by Bosch, El Greco, Stubbs and Hogarth, though not every room or artwork is always on show, and you would miss the garden, which is the other half of the visit. Pick a dry spell for the terraces.
Silverstone Museum suits racing fans and children, with hands-on displays and a sim suite, and a ticket valid for return visits for a year. Audio is loud in places. On major race weekends it is a different visit altogether, so check first.
In Chipping Norton
Jaffé and Neale is a good reason to stop on a wet afternoon: a long-standing independent bookshop, with a café that opens only late in the week. Chipping Norton Theatre shows films and other work through the year, and its pantomime fills the winter, so see what is on.
Warm pubs
The fires at the Bell at Shenington, the Unicorn and the Crewe Arms count as a plan in January. The Reine Deer's Globe Room in Banbury gives you its 1630s oak panelling to look at, if it is free. Combine one with the museum.
What not to try
Skip most of the old houses in winter: Broughton, Sulgrave and Chastleton are shut. Do not head for Burton Dassett, which has no café, and no surfaced paths across the hills. We have no cinema, swimming pool or soft play on the list yet.
Things to do in Banbury has more, and a day with children includes a plan for rain.