Get over to the Anglesey Bait Co. at gallows Point, just West of Beaumaris (almost part of the Filling Station) Talk to malcom any afternoon and he'll put you on productive marks.
Get to the information Centre which is part of the Pringles shop on the station car park at Llanfairpwllgwyngyllgogerychchwindrobwyllllantysyliogo-go-goch (LlanfairPG) Ask for the pamphlet about Sea Fishing. It has one side a list of Boats who take anglers out etc. whilst the other side, around an Anglesey map, has venues and instructions.
Various beaches/rock marks which will be productive but divided generally into busy/packed to near deserted by the ease of access!
i.e. Penmon Point (bottom, Eastern tip of Anglesey) Drive almost to sea, pay extra £2 toll and fight (gently through the throng) your way to a spot, to catch Mackeral queueing up to be barbecue fodder!
Further north, access through Llangoed is White Beach. Drive down very narrow lane, (praying that nothing is coming your way!) to very sparse parking. Walk down steps to beach and go right to reef (low water) and fish again for the obligatory Mackies which you can use for bait for bigger, flatter species!! Yes that's quite crowded too when word gets around about 'easy' macky fising, but position deters all but the keen and local!
Llanddwyn beach (bottom Western tip) pay a toll at the Forestry Commission gate and drive to big car park (wonder why it's big?) and walk onto huge expanse of storm beach. Don't trip over sunbathers (actually never that crowded, so big!) BUT leave non-family fishers to enjoy beach/walk along to island/penninsula which is Llanddwyn, whilst you get stuck into possible bass over Mussel bed in corner next to 'island'. Actually anywhere is good, try the Straits side next to Aber Menai.
If you want rocky/weedy stuff try marks in Menai Bridge. Easy parking in woods 400yds from Suspension bridge and walk down and through cemetry (Church Island) Bass, Wrasse on crab and worms. Expect to lose tackle!!
Get the map!! Good luck and welcome to Wales! Eat at the Gaerwn Arms at Gaerwen (J7a i think) off the A55, left at the little roundabout and next left, great cheapish food!! (no connection with the place, just like eating!)