Bear in find that it'll be pretty cold in January if you're from a warmer state.
Purbeck, (It's just Purbeck, not The Purbecks) is well worth a look.
From Bournemouth use the Sandbanks Ferry for the full Purbeck experience.
Swanage is a bit ho hum, but does have a steam train that will take you to Corfe Castle.
Check out the Castle and village, have spot of lunch in the Fox and then take a walk along the hill back to Swanage via Nine Barrow Down.
If you're on Purbeck during the week, go to The Square and Compass in Worth Matravers for a pint. (rammed full of tourists and 2nd home owning arseholes of a weekend).
While you're there, take a walk to St Aldhem's Chapel.
If it's running, have a go at the boat trip from Poole Quay to Swanage and back, taking in the iconic Old Harry Rocks.
Forget Stonehenge, it looks better on Youtube
Looks even better here.