I've got a new Perm (and a Calendar event in 2011) which involves riding from Connah's Quay to Bangor and back. It's possible to avoid the A55 entirely, which is something you would definitely want to do on a bike. I find the quiet roads alongside, and certain bits of cycleway, are OK and you can make good progress on them.
The stretch along the coast from Llandulas to Colwyn Bay saves the climb through old Colwyn, and the only hazard to avoid are the leisure cyclists - that and the sudden extremely steep (but short) climb and descent which come as a real surprise.
I couldn't believe what happens at the Rhos on Sea end, where the cycleway just stops, with no drop curb to get back on the road, and no parking restriction to stop motorists parking right across the end of the path. But hey, these local authorities aren't to know we need such things.
Those new bridges at Pen-y-clip are ok (at £1million a piece they should be), but the housing estate at the Llanfairfechen end seems unnecessary but sadly unavoidable. My Audax route goes over Sychnant Pass in a westerly direction but uses the old Telford tunnel when returning. Now that part of the cycle facilities is really poor - a narrow footpath, some sharp corners crossing a rail bridge, and 70mph traffic a wing mirror away.
The A55 is a perfect example of a motorway built on the cheap, with non-motorway traffic having to do the best they can. It's taken years but I think the cycle access along the North Wales coast is a viable option, and it's quite an adventure in finding your way but I hope my route sheet will be up to the task.
So that's the LlanfairPG 400 from Stockport to Holyhead and back