I have 15 days to have a looksee around this bit of England.
I`ll be using public transport and I`m hoping for advise on where to base myself.
I believe there is a terrific train that hugs the coastline?
Or should I consider car hire?
Maybe I can start in one place and end up in or near Wales.and if I went to Wales what is the best base there?
I will be coming from and returning to London, before flying home to Australia.

>>Or should I consider car hire?<<

You don't need, nor necessarily want, a car in Bath. But for touring many parts of Devon and Cornwall driving is semi-essential. Especially if you want to get off the beaten path at all. But there are areas one can tour by public transport.

Where to tour and where to base partly depends on whether you'll have a car or not. So that is probably decision #1.

Ok I`m happy to hire a car for one 7/10 days ,so over to you janisj

Tintagel, Boscastle & Port Isaac (Doc Martin) are my favourite places in Nth Cornwall

Falmouth is easily reached by train from the mainline at Truro and a great base for a few days without a car. There are foot ferries to drop you up and down the river and a good bus service as well as the train.

If you rent a car, the north coast of Devon is just lovely and scenic - the Lynmouth area is a favorite of mine - just gorgeous walks and drives.

http://www.lynton-lynmouth-tourism.co.uk/

How lucky you are to be going to Devon and Cornwall and I agree with janisj that if you can you should rent a car. There's a lot of ground to cover, could you tell us what your interests are: history, beaches, gourmet food experiences, cities, villages, etc.? Personally, I love Dartmouth. Park your car as soon as you get there by the tourist office and just wander. If you like Agatha Christie, you can take a boat from Dartmouth to Greenway Quay, and then return by boat. You can also take a steam train to Totnes. Salcombe a beautiful area. Kingsbridge a good visit on market day. Plymouth is huge, best to park and ride if you visit. In Cornwall, a great house to visit is Lanhydrock, Cotehele is also interesting. Best beach at Widemouth Bay. We stayed for a week in Westward Ho in north Devon, beautiful area. Have a great time.