"What they're saying is that last night Voldemort turned up in Godric's Hollow. He went to find the Potters. The rumor is that Lily and James Potter are -- are -- that they're --- dead."
     -- Minerva McGonagall
 

Godric's Hollow is a Muggle village¹ where James and Lily Potter were hiding from Voldemort in October of 1981. We know very little about it. We do know that they lived in a cottage there which was destroyed when Voldemort attacked them.

Some have suggested that the name of the village comes from Godric Gryffindor, one of the founders of Hogwarts and the founder of Gryffindor House, to which Lily and James belonged (Sch2). (Rowling appeared to have confirmed this in the first Newsround interview.)

In the mid-1300s, Godric's Hollow was the home of Bowman Wright, the inventor of the Golden Snitch (QA).

According to published reports, Rowling had direct input into the scene in the first film. If so, we can glean the following facts:

• Lily and James were living as Muggles in a two story cottage
• We never see James in the final confrontation, which adds fire to some of the other speculations about who was actually there.
• As Voldemort strides toward the cottage, he appears to be alone

On the evening of October 31, Voldemort attacked the Potters in Godric's Hollow. This was just before midnight. Hagrid arrived shortly after the attack and rescued the infant Harry from the ruins of the cottage. He also met Sirius Black there and borrowed his flying motorcycle. All this happened within a fairly short time of midnight, October 31, 1981. 

In the next few hours, Hagrid took Harry somewhere. We have no idea where he took him and we don't know the speed of a flying motocycle so we can't even estimate how FAR he took him. But I think it's unlikely that he stayed anywhere near Godric's Hollow, since that was 1) swarming with Muggles, and 2) the scene of the disappearance of Voldemort, which would mean that the Death Eaters were also probably all over the place, looking for their master. Hagrid left Harry in this place, wherever it is, in the very early morning. Sometime after that, but still in the early morning, Hagrid encountered McGonagall. Surprisingly, Hagrid told her practically nothing at all about what 
had happened. He didn't tell her that the Potters had been killed, he didn't tell her that he had rescued Harry or where he had taken him, he basically told her nothing. All he did say was that Dumbledore was going to be in some place called Privet Drive at some point that day. Hagrid didn't even tell her who lived in Privet Drive or what their relationship was to all that was going on. McGonagall goes to Privet Drivet at this point as a cat and waits all day on the garden wall.

We don't know where Hagrid went after this. We don't know at what point he was given Harry back to carry to Privet Drive. We might assume that wherever Harry was, he wasn't with Dumbledore, since otherwise Dumbledore wouldn't have needed someone to bring the baby to him. However, since Dumbledore obviously apparated into Privet Drive, and since it seems unlikely that anyone can carry a baby when apparating, and since Hagrid certainly doesn't have a license to apparate, Dumbledore might have given Harry to Hagrid for safe transport from wherever they were to Privet Drive. 

At any rate, this unidentified place, where Harry spent the day, is where Harry and Hagrid were coming from and it is on this trip that Harry fell asleep. And since they passed over Bristol on the way from there to Surrey, it is logical to assume that Harry spent the day somewhere 1) in Wales, and 2) NOT Godric's Hollow. So Godric's Hollow is very likely NOT in Wales at all; Wales would be a place that is a safe distance AWAY from Godric's Hollow, which would be a dangerous place to be on that day, especially for Harry Potter.

That brings us to Privet Drive. It is almost midnight when Dumbledore finally appears, and Hagrid arrives soon after. It is 24 hours since the attack in Godric's Hollow and Harry and Hagrid have traveled a good many kilometers in between.

Additional information from the web: The Mystery of Godric's Hollow Location

1 - we can assume that Godric's Hollow is a Muggle village because it is clearly stated that Hogsmeade is the only all-Wizarding village in Britain.

A note about the name and the connection to Godric Gryffindor:
In the first Newsround interview (Nr), Rowling seemed to confirm that the two are connected. Here's the exchange:

Q: And I’m going to ask one other question which you’ll say isn’t clever at all. The significance of the place where Harry and his parents lived, the first name - 
A: Godric Gryffindor. Very good, you’re a bit good you are, aren’t you?