Rain is not a write-off here. The Old Town was built for weather like this.
Morning: the museum
Poole Museum on the Quay, free, several floors, and the 2,300-year-old Poole Logboat pulled from the harbour mud.
Late morning: the Old Town, briefly
The Cockle Trail is marked on the ground and takes ninety minutes dry. In rain, do the short version and duck into the galleries and independents. See Old Town.
Lunch: take your time
This is the day for a long one. Pubs and bars in the Old Town, or a harbourside table watching the rain move across the water. See restaurants.
Afternoon: dry options
The Dolphin Centre for shopping, or afternoon tea somewhere with a view.
Evening: a show
Lighthouse runs a concert hall, theatre, studio and cinema under one roof. See theatres.
More ideas: wet weather fun.