I know Ynys Mon was an important religious place during pre-roman times in Britain, but just how important? I have some piece of trivia bouncing around in my head that says that Ynys Mon could see visitors from as far away as beyond Britain like it was some ancient Celtic Mecca. Is this true? How important was it? What do we actually know about the place?
It's difficult to really assess the importance of Mona in pre-Roman Britain. The fame of the island in relation to Druidism comes from Tacitus' Annals and its accounts of the battle between Romans and rebel Britons in 61 CE.
[Suetonius Paulinus] therefore prepared to attack the island of Mona which had a powerful population and was a refuge for fugitives. [...].
All around, the Druids, lifting up their hands to heaven, and pouring forth dreadful imprecations, scared our soldiers by the unfamiliar sight, so that, as if their limbs were paralysed, they stood motionless, and exposed to wounds. [...] A force was next set over the conquered, and their groves, devoted to inhuman superstitions, were destroyed. They deemed it indeed a duty to cover their altars with the blood of captives and to consult their deities through human entrails.
That's not a lot : we learn that Mona was a center of resistance against Roman rule and that it was associated, not necessarily centered, with Druids and "sacred grooves" themselves associated with Gaulish or British sanctuaries. Of the religious importance of Mona, we have nothing while Tacitus is really remniscent of Cicero's Pro Fonteio (XIII), a monument of bad faith and anti-Gaulish prejudice, and from Tacitus's own description of the site of Teutobourg (I, 61). Eventually, the reality of the scene might be put in question at least in part, Tacitus' reliability on Britain being sometimes considered unreliable by default.
Were people mentioned there actually druids? It's possible, for Jean-Louis Brunaux, that we might consider them as "sort of" druids, degraded leftovers of Druidry and mere magicians, prophets and other "magi" found in Britain and Gaul after the roman conquest. It's true that he's notoriously skeptical of any mention of surviving druidry in Britain or even Ireland, but it's true that the text is hardly hinting at a major influence of Mona or Mona's druids in Britain, especially as other mentions by Roman authors of the island (Tacitus' Agricola, 14 and 18; Dio Cassio's History 62 7-8; Pliny IV 30-2) don't say anything about druids or sanctuaries, but describing how Britons gathered in the island against Romans. As far as it can be told from primary sources, the military aspect of the island far outweighted others : whoever these druids were, they simply might have accompanied revolted warriors in their assembly/gathering on Mona.
Archeologically, the insular lake of Llyn Cerrig Bach was the site of votive deposits for the late Iron Age, and one of the most important of Britain known so far and second in Wales to Llyn Fawr in South Glamorgan, continuously used between the IInd century BCE and the Ist century CE contrary to the latter : there were found several artifacts, most of them of warring nature and deliberately damaged (as it was the norm in Gaul before the late IInd century BCE which does highlight the spiritual connection with Gaul; while deposits of the sort can be found in lakes and bogs across Britain) many of them being traced to south-western Britain, maybe from Irish provenance as well along with locally produced objects.
It's not clear how these artifacts went there : Barry Cunliffe argues in favour of a theft of votive objects being re-offered to the gods of their own people (not unlike the "translation" of relics in Middle-Ages); while Miranda Green does argues for an important sanctuary where chiefs of Britain went into sort of votive pilgrimage. The problem with there would be the absence of parallel in continental sanctuaries, generally associated (including in the proto-urban makeup) with a distinct people : the locus consecratus of Carnutes (assuming Mona was that for Britain, which remains unlikely at best) wasn't necessarily, quite possibly not a sanctuary, neither a votive deposit, in spite of being the place of the annual meeting of Gaulish druidry.
Altough Mona is still regularily described in pop-history as a "druidic center", not only this isn't obvious both historically and archeologically, but this identification often comes from an assessment of sources both distorted and uncritical, conflating with Caesar's account on some Gaulish druids going in Britain for improving their knowledge (possibly not, contrary to what Caesar accounts for, because Druidism originated from the island than because "conservative" druidry fled there further from Roman influence in late independent Gaul)
The site of Llyn Cerrig Bach however is authentically important in the region, even if this importance is difficult to discern. Did this importance factored in the decision gathering rebelling Brittons in the island? Did it played a role into druidic or pseudo-druidic presence, or a possible female priesthood as described by Tacitus during the first battle? That's not impossible, but remains so far speculative.