Although most thunderstorms produce rain, most rain does not have associated lightning, so one should expect that there are places with rain and snow but little lightning and thunder.
From an eyeball comparison of worldwide lightning strikes and precipitation maps, it looks like coastal Alaska and northern British Columbia, southern Chile and most of the Southern Ocean between 45°S and 60°S (e.g. the Kerguelen Islands) are the places with the most lightning-free precipitation, with coastal northwest Europe not far behind.
Pretty much any place in on a west coast at latitudes between 45° and 60° North or South will have lots of precipitation but little lightning. The prevailing westerlies off the ocean bring frequent precipitation, but the surface rarely gets hot enough to generate classic thunderstorms.
The Arctic and Antarctic have even less lightning but also little precipitation. Polar lightning strikes have recently been increasing, however, probably due to increased temperatures from the polar amplification of global warming.