About not lighting outdoors - Aruch Hashulchan (Orach Chaim 671:24) says:
והנה עתה אין אנו מדליקין בחוץ. ואף
שאין סכנה אצלינו, מכל מקום כמעט הוא
מהנמנעות, מפני שבכל המדינות שלנו ימי
חנוכה הם ימי סגריר, גשם ושלג ורוחות
חזקים. ואי אפשר להניחם בחוץ, אם לא
להסגירם בזכוכית. וכולי האי לא אטרחוהו
רבנן. ועוד: דבזה לא יהיה היכר למצוה כל
כך. וגם לא בכל המקומות יניחו לעשות כך.
Nowadays we don't light outdoors. Even though there is no danger in our areas, nonetheless it is almost impossible to do so, since in all our countries Chanukah is during the wintry season, when it's rainy, snowy, and there are strong winds. It would be impracticable to put them outdoors unless they were enclosed in glass; our Rabbis did not want to burden one to that extent. Also, the mitzvah would be less noticeable that way. Furthermore, they [the local authorities?] may not allow one to do so in all places.
About lighting by the door - there is the advantage (mentioned in Shulchan Aruch, Orach Chaim 671:7) of being "surrounded by mitzvos," with the mezuzah on one side and the menorah on the other.
In one of his letters, the Lubavitcher Rebbe zt"l points out that lighting at the window has a couple of disadvantages: (a) frequently the window is over 20 cubits from ground level, in which case it's anyway not noticeable by people outdoors, and for the people in the house it would be more visible at the doorway; (b) many Chanukah menoros have a back panel behind the lights, and in that case, there's no way to place it on the windowsill such that both the passersby and the dwellers in the house will be able to see them.