Moors Valley country park ( has a lovely play trail and playground)
Go Ape at Moors Valley
Beaulieu (museum with play park/monorail etc)
Bucklers Hard
Hengistbury Head (there's a land train, visitor centre and a lovely cafe)
Ferry to Isle of Wight
Wilverley Plain or Bolderwood deer sanctuary both good for animals ( deer, cows, ponies etc) although ponies everywhere to be fair !
Afternoon tea at Chewton Glen ( various hotels offer it)
New Forest reptile museum
Exbury Gardens and steam railway
Furzley gardens
Longdown activity farm
Crabbing at Mudeford (also ferry across Quay)
Tuckton tea gardens has boats you can hire to go up and down the river
Hire bikes at Burley. They give you a map of suggested routes.