First, the local truth about Cork weather: it tends to come in showers rather than a steady all-day downpour, and the centre is small enough that you're never more than a couple of minutes from cover. An umbrella and decent shoes are all you need. Taxis are cheap and quick for the two or three hops that aren't covered.
Morning: the market, under a roof
Start at the English Market. It's fully covered, it's been trading since 1788, and on a wet morning it's the warmest, liveliest place in the city. Do a slow lap of the stalls, then go up to the Farmgate Café on the balcony for breakfast looking down over the whole market. You could happily lose an hour and a half here before you've even stepped back outside.
Late morning: a proper museum
Two good options, both indoors. Cork City Gaol, the restored prison up at Sunday's Well, is if anything better in the rain, atmospheric and completely under cover once you're inside; take a taxi up so you don't do the hill in the wet. Or, if you'd rather stay free and central-ish, the Cork Public Museum in Fitzgerald Park tells the city's whole story and costs nothing. Either one is an easy hour or so, and both are written up on our museums page.
Lunch and afternoon: Nano Nagle Place
Head to Nano Nagle Place off Douglas Street. It's built around a sheltered courtyard, with a museum, a bookshop, and one of the nicest cafés in the city, so you can eat, browse and take in the exhibition without going back out into the weather. It's a genuinely calm spot, and easy to lose the middle of the day in. If you'd rather something shorter, the Butter Museum at Shandon pairs with an indoor climb up the Shandon Bells tower.
If you need more cover
When the rain sets in properly, Cork has plenty of dry bolt-holes. There are two large shopping centres in the heart of town, off Patrick Street and over on St Patrick's Quay, and good bookshops for an hour out of the weather. The free Glucksman gallery out at the university is another warm, quiet hour if there's a show on. The Gate cinema shows current releases if you fancy sitting a shower out in the dark, and the Everyman and Cork Opera House often have an afternoon or early-evening show worth checking. And there's always another café, Cork takes its coffee seriously, so ducking into a warm one to wait out a heavy burst is a perfectly good use of twenty minutes.
Evening: a fire and a session
End the day the way Cork does a wet evening: dry off over dinner somewhere snug, then find an old bar with a fire, no screens, and live trad. Places like the Mutton Lane Inn, tucked down its own alley off Patrick Street, or The Long Valley are made for it. By now the rain is someone else's problem.
What about the tour?
The walking tour runs rain or shine, and we keep umbrellas for guests, so a wet forecast is no reason to skip it. If anything, Cork under a bit of rain has its own character, and the stories are just as good with a brolly up. See the walk and times. Got the kids with you? The Cork with kids page has the indoor family options too.