Tank Museum &/or Monkey World – Bovington. Both much better than they sound (really really good).
Lulworth a bit overrated – try Winspit or Dancing ledge instead followed by a visit to one of the best pubs in the world, the Square and Compass at Worth Matravers.
Drive to Corfe, walk to Swanage over Nine Barrow Down and Ballard Down – lunch in Earthlights Cafe then get a steam train back.
Get a ferry from Poole Quay to Brownsea Island.
Get a ferry from Mudeford Quay, walk round Hengistbury Head, then get the ferry back and buy a pint of prawns to eat while offspring catches crabs with a handline off the quay (do 13 year olds do that anymore – I did!)
Or nearer to Wimborne, Kingston Lacy House is nice and Badbury Rings is a good place to walk.
Or Go Ape! at Moors Valley Country Park
Or on a Tuesday Salisbury has a really good market + an amazing Cathedral + good places to eat (such as Snells Tea Rooms
I could go on….