I'm not a library of Anime shows, so this is a difficult task for me.
Find a show that has;
*Great, enjoyable plot.
*Well designed characters.
*DOESN'T constantly tease the viewer with a potential relationship that never delivers.
*Isn't just comedic relief or completely bonkers.
Can you be a bit more specific on what genre you enjoy?
Since you mentioned 'no teasing with a non-delivering relationship' are you looking at romance stories?
The Melancholy of Haruhi Suzumiya - 2 series and a movie. A high school relationship tale with a difference. Make sure you watch the first series in the broadcast order which is a non-linear
order and makes the story more confusing but adds much more impact.
Mawaru Penguindrum - a family crisis of bizarre proportions and causes. Same director as Revolutionary Girl Utena so expect a weird and wonderful ride.
Hyouka - very cute and with a lovely ending. Very pretty artwork.
Usagi Drop - something very, VERY different. A slice of life story of a 30 year old single man suddenly facing bringing up a 6 year old girl. I found this terribly touching, made me cry a lot!
Koi Kaze - a rather blunt and at times disturbing look at older brother/younger sister incest. Not for the sexually prude!