How much of a magical establishment is Godric’s Hollow? It’s supposed to inhabited by wizards, I think. But I vaguely remember muggle children being mentioned the night Voldemort broke the fidelius charm. Does this mean that muggles can come and go? James and Lily’s cottage was also charmed to be hidden to muggles, right? So, Godric’s Hollow is only partially a wizarding establishment?
Primarily a muggle town, but several wizarding families do reside there. So yes, you are correct. :)
The square is a muggle square, statue, church and cemetery and houses all around. But yes the Potter’s house/monument were charmed.
Bathilda Bagshot’s note that Godric’s Hollow is the home of a relatively large number of wizards does not indicate that it is a purely Wizarding village; in fact, Hogsmeade village is the only purely Wizarding village in Britain. As such, wizard residents of Godric’s Hollow must still avoid open use of magic to avoid disturbing the Muggle residents of the village. This is why the monuments to the Potter family must be hidden: the sculpture of the family appears to be an ordinary cenotaph except at certain angles, and presumably only wizards can see it at all.
Similarly, the Potter cottage on the edge of the village is charmed to be invisible to Muggles. One must assume that a charm similar to the one that hides 12 Grimmauld Place must be in use at the latter site, to prevent Muggles from trying to build on the apparently empty lot as the village grows. Given the Dumbledore family experience with Muggles, it is a little surprising that the family chose to settle at Godric’s Hollow rather than Hogsmeade. However, it is possible that there was some family history that connected the family to this village; and it seems likely that the Dumbledore family chose to live in a part of the village that was primarily wizard-occupied.
In A History of Magic, Bathilda Bagshot writes that Godric’s Hollow is one of a number of villages where wizards settled in relatively large numbers after the ratification of the International Statute of Secrecy in 1689. It appears that the Dumbledore family moved to Godric’s Hollow when Albus Dumbledore's father Percival was imprisoned. Albus and his mother Kendra, sister Ariana, and brother Aberforth lived here, until Kendra’s and Ariana’s deaths. At the time, Bathilda Bagshot was their neighbour. Godric’s Hollow was famed as the birthplace of Godric Gryffindor, and also as the final resting place of at least one of the Peverell family.