No special access issues
From the end of the promenade in Llandudno, take the road out around the Marine Drive (toll road) and very shortly after the toll booth, after a cattle grid, the cave becomes very obvious on the left hand side. There is parking here for about six vehicles, so it can be worth checking on busy days by parking just before the toll booth - and thus saving a few quid - and walking around the corner to check for spaces.
Split Infinity Cave is a little further on to the right. Breck Road can be found up the hill to the left of the cave proper.