Don't drive as of yet. Historical places would be great,and I've been told by locals there are some fab beaches around here with lovely sea!!!
Bournemouth has quite a nice beach, also there's Lyme Regis and Weymouth. For historical places, you're spoilt for choice. There's Corfe Castle and Swanage, Sherborne Abbey, the Rude Man of Cerne Abbas, Maiden Castle, Thomas Hardy's two houses, lots of National Trust properties (Kingston Lacey is lovely), Abbotsbury, Shaftesbury, and Dorchester are nice historic towns, and of course you're also close to the New Forest, though that's in Hampshire
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. Also in Hampshire are Southampton and Portsmouth, which are both interesting cities. Lots of places are accessible by train, though for many of them it's best to drive. There are also things like food festivals and markets and other festivals, etc. I love Dorset!