The forecast matters less here than people assume, provided you have a plan for both.
If the sun is out
Beach early, before the car parks fill. Watersports on the harbour mid-morning. A boat to Brownsea or across the chain ferry to Studland in the afternoon. Dinner on the Quay.
If it is raining
Poole Museum, free, several floors, Iron Age logboat. The Old Town galleries and independents. A long lunch in a pub that predates the weather forecast. Lighthouse in the evening. See wet weather fun.
If it is somewhere in between
Which it usually is. The chine walks are sheltered by trees. The harbour shoreline is flat and does not mind a shower. And a grey harbour with the light coming through is better photography than a blue one.
What to pack regardless
A windproof layer. Poole is on the water and the wind comes off it whatever the temperature says. See weather.