please do quote me on this, but I may suggest the castle car park, well I call it the castle because that's what it looks like, there is a large car park there and last time we visited the place there were tree smallish motorhomes, having had a chat with them I established that they had actually parked there 2 nights with no problems at all, that was last year, hence above do not quote me, it may well have changed now, also on the main road keeping the castle on your left I saw parking space to the right of the road, good luck.
by far the best site in the area. caravan club site on the coast overlooking north Wales
http://www.ukcampsite.co.uk/sites/details.asp?revid=5424
Have a look on google earth, 10min drive from New Brighton.
Was at New Brighton yesterday Sunday spoke to a MHer on the car park it,s called" Fort Perch Rock " he said there were 5 vans parked sat/sun with no problems also other vans parked near the marina again no problems, go for it,it,s on my list and it,s free there there is lots of entertainment ,pubs, eating places, much improved, very busy weekends