The coffee in Poole is better than a seaside town has any obligation to provide, and the delis are worth a detour if you are self-catering.
Where to find it
The Old Town has the independents, tucked into the lanes behind the Quay. Ashley Cross has the concentration, and Canford Cliffs the smart village version. The Quay itself does breakfast with a harbour view, which is its own argument.
Beach cafes
Every main beach access point from Sandbanks westward has something, from a kiosk to a proper sit-down café. Most are seasonal, so check before relying on one in February.
Delis
If you are in self-catering, the delis and farm shops around Poole and out towards Wimborne are where to shop. See also afternoon tea.