"The high places" is the standard translation of the Hebrew word bamot, but it is not clear that height was an intrinsic feature of these worship sites. The idea is simply that of publicly accessible structures (including unenclosed altars and temples with altars) within which or on which offerings were made to God or the gods. The continuation and proliferation of these local places of worship (as opposed to the one place of worship described in Deuteronomy 12) is one of the main concerns of the authors of 1 Kings + 2 Kings. Solomon begins by tolerating worship of the Lord at these places and ends up being drawn into full-blown apostasy, as later do Israel and Judah.
(The ESV Study BibleTM, English Standard Version (ESV) by Crossway Bibles, 2007. Page 597)
The great high place was in Gibeon.
(1 Kings 3:4-5)