Poole has more accessible green space than a town this size has any right to, and most of it is free.
Poole Park: the family one
Victorian, built around a saltwater lake fed from the harbour, with a miniature railway, play areas, flat paths and open grass. Free to walk into; boat hire and the railway are charged. Between the town centre and Parkstone, walkable from the station. See Poole Park.
Compton Acres: the designed one
A sequence of themed gardens at Canford Cliffs, Italian and Japanese among them, laid out on a slope above the harbour with a tea room attached. A paid attraction, and the only one on this list, but the setting does a great deal of the work. Allow two hours. See Compton Acres.
Upton Country Park: the quiet one
Parkland, formal gardens, woodland and harbour shoreline around a Georgian house, on the quiet north-western side of the water. Free entry, parking charged, level paths. In winter the mudflats here fill with waders. See Upton Country Park.
Hamworthy Park: the one with a beach
Grass, a playground, a paddling area and a shallow harbour beach behind it. Free. The best option in Poole with under-fives.
Arne: the rare one
Across the water, lowland heath of a kind that has largely vanished from Europe, with species that live almost nowhere else in Britain. Keep to the paths: much of what lives here nests on the ground. See Arne.
More ideas: parks and gardens and family fun.