Welcome Paddy.
As Mike has already suggested, there is a good chance of a Flounder in Rhyl harbour.
You should be able to find somewhere dry to fish at any state of the tide and with the crabs not peeling yet, you will have a good chance if you use worm baits. Maybe try the new quay wall on the Kinmel Bay side over high ( across the Blue bridge, 1st right past the pub and camp entrance, over the speed humps and you come to the wall and parking area ), or move onto Hortons nose ( the sand dunes ) and fish into the pool ive circled over low.
http://www.multimap.com/s/jpdxMn56
Splash Point is the other option, but from what you are asking for, you would have to fish it at high water, which might interfere with your drinking or hangover.
Theres is the chance of Dabs or even a Codling here, but Whiting have been very thin on the ground all along this coast since Christmas
There are plenty of Rockling here to keep you amused.
http://www.multimap.com/s/giYzLp0C
Tide times for Rhyl are;
7/3/09, High water 07.28 25.3ft. Low water 14.27. High water 20.12 25.9ft.
8/3/09, High water 08.39 27.6ft. Low water 15.34. High water 21.13 28.2ft.
Tight lines wherever you go.