Poole is a working fishing port, not a seaside town that happens to serve fish, and the distinction shows up on the plate.
What the harbour produces
Shellfish, principally. Poole Harbour has been associated with oysters and clams for centuries, alongside scallops, crab and the day boat catch landed on the Quay.
Where to eat it
The Quay is the obvious answer and the best one for a first visit: terraces looking at the water, menus built around what came in, and the boats a few metres away. Busiest in summer; the view is part of what you are paying for. See restaurants.
The Old Town immediately behind it has the smaller rooms, where the menu is short because one person is cooking it. See Poole Old Town.
Ashley Cross is where locals eat year-round, and several kitchens around the green do seafood properly without the waterside premium.
When it is best
Shellfish seasons vary by species, and any kitchen worth eating at will tell you what is good that week rather than serving the same card all year. Ask.
Beyond the plate
If you want to see where it comes from, the boat trips from the Quay take you out across the harbour the catch is landed from. See also food and drink experiences and the best foodie finds in Poole.