To get to Lyme Regis, you can take the A35 if you are driving from Dorchester or Bridport. From Exeter, take the A3052 towards Sidmouth and follow that until you reach Lyme Regis. If you prefer to take the train, you can catch a direct train from London Waterloo station to Axminster, and then change to a bus for the short journey to Lyme Regis.
If you are already in the Dorset area and looking for a day trip, consider visiting the nearby town of Charmouth, which is just a few miles away from Lyme Regis and has a beautiful beach and scenic coastal walks. Alternatively, if you are looking for a larger city, Exeter is approximately 30 miles away and has plenty of attractions including historic landmarks and excellent shopping opportunities.