Hi,
Welcome to the site.
There are spots on the Little Orme and the Great Orme in that can be fished. The climbs down to these can be a bit harsh and i would be inclined to have a day in the area without the rods just walking down to a few of them and seeing what the access is like.
Most are down steep grassy slopes which makes them very tricky if wet! The rocks at the bottom arent too bad to fish from and the fishing can be good depending what sort of species you are after. Mainly Dogs with the odd Huss, Ray or Smoothie and plenty of Wrasse and Pollack down the side.
If its big fish youre after, dont over look Perch Rock at New Brighton where there are Ray and the odd Smoothie showing at the moment and its a lot closer to home for you. There are also big Conger at Mostyn.
If you want further info on the Orme marks let me know and ill give you a few spots to look at.