You managed to get me to at least skim through my archive despite it being past 2 o'clock in the morning around here. There were four titles that caught my eye immediately.
So I'll just throw them at you before wandering off to sleep.
Jin-Roh (Or Jin-Roh: The Wolf Brigade). This is not something you should watch if you're (just) looking for a good time. The film is by far too dark for that.
"Origin - Spirits of the Past" and "Wonderful Days" (Sametimes listed under Sky Blue). Those two are somewhere in between the the first and the last when it comes to the "grim and gritty" factor (or the absence of humor). Still adressing serious topics (ecological questions and morality decisions).
The last one is mostly for fun in my book: Howl's Moving Castle. I'm aware it still adresses some interesting issues - actually no less serious topics than the other three - but a lot of the movie is simply amusing to watch along the way.
Edit: Just re-read my post and realised this is a prime example of "why i shoud NOT write posts at half past two in the morning". I'm sorry.
If you stumble across any typos, you may keep them and rear new ones in your basement.