Jamieson, Fausset and Brown on Deuteronomy 12:2

2. Ye shall utterly destroy all the places, wherein the nations which ye shall possess served their gods--This divine command was founded on the tendencies of human nature; for to remove out of sight everything that had been associated with idolatry, that it might never be spoken of and no vestige of it remain, was the only effectual way to keep the Israelites from temptations to it. It is observable that Moses does not make any mention of temples, for such buildings were not in existence at that early period. The "places" chosen as the scene of heathen worship were situated either on the summit of a lofty mountain, or on some artificial mound, or in a grove, planted with particular trees, such as oaks, poplars, and elms (Is 57:5-7; Ho 4:13). The reason for the selection of such sites was both to secure retirement and to direct the attention upward to heaven; and the "place" was nothing else than a consecrated enclosure, or at most, a canopy or screen from the weather.