For Harry Potter related location questions, a good place to start is Location, Location on the White Hound Fanfiction site. They try to consider all the existing clues, fairly neutrally, and often give a surprisingly precise location of the relevant place even based on a very few clues.
For Godric's Hollow, in particular, they give some more details than just "West Country":
We can also say that Godric's Hollow is probably towards the north side of the West Country, or at any rate not on the southern side, because if it were on the south side then going via Bristol would involve a considerable detour.
This rules out Dorset (which is too far south). Cornwall is unlikely for linguistic reasons (it's too Celtic, and would not have Anglo-Saxon place names such as Godric's Hollow, especially not in the Middle Ages).
They note then one crucial passage that had not been mentioned in any of the answers previously:
'But what if I'd given Harry to him, eh? I bet he'd've pitched him off the bike halfway out ter sea.' [PoA ch. #10; p. 154]
The phrase "halfway out to sea" does not make much sense for something right on the coast (it's either to sea, or it isn't), and does not make much sense for something very far from the coast (as halfway to coast would still be well on land). They then consider when would that phrase make sense, and then several other geographic clues; I will not summarize any more (it is better to just read the linked article itself).
Their end result, however, is well worth quoting:
The most likely location for Godric's Hollow is somewhere near Weston-Super-Mare in Somerset: either near (but not on) the coastline facing into the Severn Estuary, or on the estuary of the River Parret which feeds into Bridgewater Bay a few miles south-west of Weston-Super-Mare. Hagrid passed over Bristol en route to Little Whinging because he used the motorways as a guide, picking up the M5 near Godric's Hollow and following it to Bristol, and then the M4 from Bristol to Heathrow.
(They have figured out that Little Whinging is near Heathrow in a separate article. I will not describe their reasoning in detail here, but basically it is the only part of Surrey that is remotely near the described railway.)
They do not appear to have considered the tiny triangle NW of Bristol - which is strange as they typically consider all possibilities, however unlikely. It definitely fits their clues (including the "halfway to sea" one) just as well (as far as I can tell, anyway).
As for the wild moors - one would suppose that what was wild moors ten centuries ago might not necessarily be so today. This particular one seems to be what is now known as Sedgemoor.