One of the best is by Porth Daniel/next to the Menai Suspension Bridge.
It is V. Sheltered from almost any direction.
It is just off the A55 so easy to get to for you.
It is almost fully tidal. You can launch at nearly all tides. (Though this week end are some of the largest tides of the year, 7.6m! so it won't be fully tidal this week end!) On the plus side they are at 1pm so you can right up in to the bays.
You can travel either NE or SW depending on which way the wind is and be protected. It would take about 25 mins at 30mph (ie 12-13miles) to get up the straits and round to bennellech, after seeing the seals and puffins at Puffin Island.
It is a slip owned by the council so you only need to register with the council at the site below, giving access to many other slips at beaumaris etc and it costs for the year:
How much does registration cost?
From the council direct - £15
At the slipway - £20
Customers who do not buy a seasonal launch permit with their registration will need to pay the registration fee plus the day's launch fee on their first launch. On subsequent launches they will only pay the daily fee.
Give then a call and ask them what the score is.
Have fund. I'm around Fri/Sat hoping to travel from Menai Bridge to Abersoch!