On 12-13, I made some changes to this post.
Rambam writes in the fourth chapter of Hilchot Megilla V'Chanuka:
נר חנוכה, מצוה להניחו על פתח ביתו מבחוץ, בטפח הסמוך לפתח, על שמאל הנכנס לבית--כדי שתהיה מזוזה מימין, ונר חנוכה משמאל; ואם היה דר בעלייה, מניחו בחלון הסמוכה לרשות הרבים.
The Chakhamim instituted that candles be lit outside near the entrance of the house right next to the left side of the door, as one enters the house. Rambam seems to add an unnecessary clarification when he tells us that this is in order (or so) that the m'zuza will be to the right and the Chanuka candle to the left. Why does it matter where the Chanuka candle is placed? Would it not have been enough to just light it outside? Why is it important that the m'zuza is to the right and the candle to the left of the entrance?
As was discussed in the previous post, the purpose of lighting candles on Chanuka is for each Jewish household to commemorate the miracle of the oil and thereby demonstrate its loyalty to the ideals of Mikdash. In order to understand why the Chakhamim decreed that the candles should be lit near the left side of the doorway opposite the m'zuza side we must explore the mitzva of m'zuza in greater depth.
Rambam writes concerning the m'zuza:
וכל עת שייכנס וייצא, יפגע בייחוד שמו של הקדוש ברוך הוא--ויזכור אהבתו, וייעור משינתו ושגייתו בהבלי הזמן; ויידע שאין שם דבר העומד לעולם ולעולמי עולמים, אלא ידיעת צור העולם, ומיד הוא חוזר לדעתו, והולך בדרכי מישרים. אמרו חכמים, כל מי שיש לו תפילין בראשו ובזרועו, וציצית בבגדו, ומזוזה בפתחו--מוחזק לו, שלא יחטא: שהרי יש לו מזכירין רבים; והן הן המלאכים שמצילין אותו מלחטוא, שנאמר "חונה מלאך ה' סביב, ליראיו; ויחלצם" (תהילים לד,ח).
To paraphrase Rambam: the m'zuza is placed on the doorway so that every time a person walks in and out of his house he will be encounter the idea of the unity of G's name and he will be awakened and will be reminded that the only thing that stands forever and ever is the knowledge of the Rock of the Universe and this will lead to a re-framing of one's mindset and will cause one to live a proper life.
Most people relate to their house as an everlasting structure. A house is a source of security both real and imagined (as discussed in this post). Through this structure man imagines that he possesses true sovereignty. As the saying goes, "a man's house is his castle". It is unimaginable to most people that one's house could, literally, fall. Yet, the only thing that stands for ever is the knowledge of G'. The doorway is the threshold between the outside chaotic world and the inside controlled environment of one's home. As one leaves the security of his house he encounter the m'zuza and is reminded of the unity of G's name - that the world is not as chaotic as it seems - it is all guided by G's wisdom. As one enters his house he is reminded that as secure and peaceful as his home may seem any sovereignty he attributes to himself is illusory because only G is the true Sovereign. The door is the perfect place for man to remind himself of the unity of G's name - on the threshold between the two spheres within which he lives - at the intersection of the private and the public, the chaotic and the controlled - man is reminded of his true credo. The m'zuza makes a statement about the character of one's household - that it is a household that does not glorify the sovereignty of man rather it glorifies the true sovereignty of G.
The doorway is the location the Torah selected for us to remember the ideals upon which our households should be founded. For this reason the Chakhamim decreed that one must light in one's doorway. In that place which the Torah instructed us to remember our most important credo - the unity of G's name - we also demonstrate our loyalty to that institution that proclaims that credo - the Beit HaMikdash. However, the ideals of Mikdash are more than just ideals that we proclaim our loyalty to - by lighting in our doorways we demonstrate on Chanuka that they are the ideals which act as the guiding light and foundation of our households.