You have a choice of several routes for getting from Oxford to Dorset. You should try and follow your various options on Google Earth.
I have driven the B3157 Dorset Coast Road which wiggles its way through small villages - but does not offer much of a coastal view as the coast here is low lying and flanked by a long shingle bank called Chesil beach. If on the B3157, I would definitely visit Abbotsbury sub-tropical Gardens. http://abbotsbury-tourism.co.uk/gardens/gallery/
Just N of Dorchester on A352, you might wish to visit the Cerne Abbas Giant.http://www.nationaltrust.org.uk/cerne-giant/
A little further N on the same route is Minterne Gardens.http://www.minterne.co.uk/mjs/gardens.html
I think that the best bit of the Dorset coast lies E of Weymouth at Lulworth & Durdle For (the arch) http://www.lulworthonline.co.uk
Cliffs and bays are also found to the west running into Devon.http://jurassiccoast.org
I found Weymouth to be rather congested.
As an alternative, you might also like to consider following the A40 west from Oxford and into southern Wales. Parts of this route traverse the very scenic Brecon Beacons National Park.http://www.breconbeacons.org
You could stay on this route all the way to Tenby in Pembrokeshire - which would be a full day's driving. (A quicker but less scenic route exists by following the M4/A48 across southern England & Wales).
Both Tenby & Lyme Regis are likely to have parking problems (narrow streets) so would not possibly be the best places to actually book accommodation - unless they can guarantee parking. Both are rather a long journey to then just spend one night. Check journey options here:>http://www.theaa.com/route-planner/index.jsp (For the scenic route from Oxford to Tenby - you would need to put VIA Brecon). Putting in the start point and destination will not necessarily be the most interesting route).