For a Briton, ‘just west of Yeovil’ means within 5 miles. Otherwise you’re ‘just east of Taunton / Exeter’ or ‘just north of Lyme Regis / Honiton’. 
You’re not going to Glastonbury, are you? Because if you’re there for the Extravaganza, that’s a whole different kettle of fish.
Yeah…as I already admitted to Filbert, to this dumb American “Cornwall” is everything west of Bristol. Which I know is sort of like saying everything west of the Mississippi River is California. (It’s not as bad as calling a Welshman “English”, though, as I did on my very first trip to Britain. He politely but firmly corrected my egregious error, which I have never done again.)
I’m actually staying in Somerset, about 25 minutes west of Yeovil. Yes, mentioning that the first week would be in London would have been helpful. So the best itinerary might be to take a coach/train directly from London to near Yeovil and pick up the car rental. At the end we’d drop off the car in Yeovil and take a coach/train to Heathrow.
I already have plans to stop at Montgomery Cheese (http://www.montgomerycheese.co.uk/) to gorge on Cheddar. Do you think that the Naval Aviation Museum is worth a visit? http://www.fleetairarm.com/
I sometimes forget that it doesn’t start just west of Yeovil, and only remember when I see Exeter on the map and remember playing a game in the 90s that mentions it is in Devon.
So somewhere near Taunton or Bridgewater? Or are you being optimistic and calling Minehead 25 mins west? Please, stop being coy and tell us where you’ll be staying. We can’t help you if we don’t know. The transport system is sufficiently - ahem - interesting that a few miles can make a big difference.
Not if you’re a fast walker