If you're just staying in Poole then probably the old quay area including perhaps a visit to Poole Pottery down there. Other than shops in the Dolphin Centre not much else to see - unless you travel a few miles?
I have an evening meal booked at the hotel and then an early night, I am just looking for a place of interest or somewhere with a view for a quick drink at least as I will be arriving about 2pm.
Then I'd think the Quay is your best bet, old buildings, pubs and eateries and some character unlike central Poole, usually bustling, good views of the harbour and Brownsea Island. Hope the weather is good for you.
It's 6 miles that will take you half an hour. I was also thinking of suggesting Sandbanks - nothing there to do except ogle some mega properties - but again that's a good 20 minutes in the car from Poole. may look close on the map but the traffic is also very heavy everywhere in Poole/Bournemouth area.
So.... Poole (in particular the surrounding areas) is a lovely place. The weather stayed dry, I drove to Sandbanks and gawped at the mansions. I then retired to the hotel which had a great view of the harbour for coffee.
There was enough going on to convince me to return (for leisure) in the near future.