Although the main tourist centres are often crowed in the holidays, you need travel only a short distance to find quiet roads.
There is a wonderful network of country lanes in Arfon, Eifionydd and Llyn, and also on Ynys Mon (Anglesey). Some minor roads have been waymarked by the local authorities as circular cycling routes. There are also Sustrans Routes, which form part of the National Cycle Network, which (eventually) connect you to the rest of Britain.
Cycling gives you the means to explore the local area, travelling slowly enough to see places that you may otherwise be moving too fast to notice.