I second the coastal cycle path, I am a regular on the Rhos to Abergele section.
Circuit of the Great Orme has great views but has hills and light traffic.
There are also a cycle paths along old railways:
1. Bangor to Bethesda: should be nice but never done it myself
2. Most of the way from Bangor to Caernafon
3. SE from Caernafon
Or if you are looking for a short one, suitable for young children, there is one along an old railway at Llanberis, parallel to the west shore of Llyn Padarn.
Another short route runs around Llyn Crafnant (above Trefriw) but there are a few cars on half of it but also a nice cafe. Should be fine for older children. Short rough hill also.