holyhead is prob your best bet for vacancies
it has good access in all weather
there is a long waiting list at peelyweely pwllellie however its spelt
i think abersoch has some moorings i think although i would imagine they are pretty exposed and probably in high demand
try the north wales cruising club
they may have some ideas and contacts
there are moorings on the Menai straights Bangor YC has those mostly
caenarfon has a small marina type thing now and i am pretty sure that is a lock so will be tidal
On the Menai Strait there are many vacant moorings both to the north and south of the bridges where people keep and pay for them but their boats are on the hard all year. To find out which are vacant you'll have to do serious investigation locally. For north of the bridges Stan Z or his son or Jonathon at Silliwen may be able to help you. South of the bridges, contact John McDermott at the Caernarfon Harbour Trust's Office on Slate Quay (next the Castle) Caernarfon.
Otherwise you may be lucky with Holyhead Sailing Club (Very nice club) and be able to rent a paid for mooring ... Or you could try your luck at Deganwy ....
As a last resort you could approach Dickies and see if you can hire a bit of their wall whilst you trawl round trying to find out who 'owns' the vacant moorings ....
Re: A usefull starting point is this link to NWVYC
Moorings at Abersoch are very busy in the summer, but give the bosun a call and ask if you can sublet one for a year - sometimes people don't use theirs and you can sub-let them. Beautiful sailing! www.scyc.co.uk
I would imagine there's moorings available in Conway. Try the Harbour Master (Tony Mead) on 1492 596253 9-5/Mon-Fri this time of year. Generally very helpful. Moorings are up for renewal about now, and run April-April.
Re: A usefull starting point is this link to NWVYC
Jonathon's moorings at Siliwen dry out.
Pwllheli is booked up.
Port Dinorwic can accomodate Your boat if You want alongside Marina facilities.
Swinging moorings by Menai contact the Piermaster.
Phone No. later tiss not to hand now!
Holyhead, nice Club, as mentioned.