I had a rental car when I stayed at a lovely AirBnB in Lyme Regis a few years back. Lovely area between there and West Bay.
Visited West Bay and strolled for hours along the beach. Also took the West Bay cliffs trail that was featured in Broadchurch.
Enjoyed the same in Lyme Regis. Try to visit the small and interesting Lyme Regis Museum.
Had Good coffee at Aroma where you can sit and watch the huge tourist busses negotiate the small road and curve to enter Lyme Regis. However, this was 7 or 8 years ago so no clue if Aroma still exists.
If you visit Lyme Regis, had some good fish and chips at Herbies on the Parade.
Lastly, Lyme Regis is hilly so be prepared to walk uphill from the Parade. Great fudge at Roly’s, found the Sanctuary Bookshop of interest and bought a gift for friends at the Pug and Puffin pet store.
If you need a pint and a cozy fire ( AND if still open ) you can find both at the Red Lion Inn.