If you go up to the top of the Great Orme there's a St Tudno's church/cemetary on the road down towards the 'toll' bit of road where there's a bit of parking outside which I would think is fairly safe and quiet! Some info on here:
When we were last there though it was extremely windy so instead of staying near the church we went down to the pier (on the east side) where there's a bit of parking next to it and we had a good night's kip along with another motorhome, whether the parking's still there though I don't know.
Just one thing to watch out for, if you aren't bothered about the first mile of the drive round the Orme (the rest of it is as good but no toll to pay!) don't go on Marine Drive on the east side (that's where the toll booth is), instead just go up to the top of the Orme and then turn right where the Tram station is which takes you down the road past the church and then onto the hairpin bends down to Marine Road ... but be warned some of the bends are VERY tight, we managed it in our Rimor motorhome at the time which was nearly 24ft long, but it wasn't easy!