Out of all Shinkai movies I'd have to pick
The Place From Our Earliest Days, because of the beautiful narration + music + scenery all in one, all while within an interesting, gloomy atmosphere. The explanation is to persuade Ledgem to watch it.
Tokyo Godfathers
Hotarubi no Mori e
ef
Kowarekake no Orgel (kudos to Kirito)
Mushishi