Wales, due to its landscape and topography, has become very popular as a destination for mountain bike holidays and indeed plain bicycle holidays. There are opportunities for relatively flat trails round the many lakes and coastal paths, or there are many more demanding courses, in the forests and hills of the Snowdonia National Park for example.
Many of the lakes in Wales including Llyn Brenig in North Wales, Llys y Fran in Pembrokeshire and Llyn Nant-y-Moch reservoir in the Rheidol Valley near Devil's Bridge offer dedicated Bike Trails either round the lakes or in the forests nearby.
This is the safe alternative to cycling on the roads in Wales. Admittedly there are going to be accidents on the mountain tracks but these will be self inflicted and with at least a bit of care should in no way be as life threatening as attempting to cycle on the roads of Wales.