In addition to the menorahs placed in the doorways and windows of Jewish homes, the sages instituted the practice of lighting the menorah in synagogues in order to further publicize the Chanukah miracle. The synagogue menorah is placed near the sanctuary's southern wall (reminiscent of the Temple menorah that was also located along the sanctuary's southern wall), and is kindled before sunset, immediately after the afternoon prayers.
Those in attendance in the synagogue, even the one who actually kindles the menorah and recites the blessings, have not fulfilled their personal menorah lighting obligation. They are still required to kindle the menorah at home.
Ideally, the synagogue menorah should be rekindled in the morning, so that it remains lit throughout the day (whenever people are present).
In times past, the synagogue was the most public Jewish venue. Today, however, the reality is such that many Jews do not visit the synagogue on a daily basis. The Lubavitcher Rebbe therefore encouraged the erection of menorahs in public areas to maximize the reach of the radiance of the Chanukah lights and to publicly proclaim the timeless message of the Chanukah victory of light over darkness.
If you are considering constructing a large outdoor menorah yourself, the maximum height of a kosher menorah is approximately 37 feet. People don't normally look up higher than that height, and a menorah taller than that wouldn't serve the intended purpose.