Built so the weather cannot ruin it.
Afternoon: the Quay
Poole Quay in the afternoon, with a harbour cruise if it is fine: see boat tours. Poole Museum is the indoor alternative, free and on the same stretch of waterfront.
Early evening: eat
Poole Quay for seafood by the water, or Ashley Cross for choice in a small radius. See restaurants.
Evening: the show
Lighthouse is among the larger arts venues outside London, with a concert hall, theatre, studio and cinema. See theatres and check what's on for dates.