Before I left for Japan the last anime I watched was
Kure-nai.
It is easily one of the best anime I have ever watched.
The character development, animation and storyline is sophisticated and almost without peer.
If you want non-stop action, then this may not interest you (although there is some vicious no-holds barred femme vs femme MMA action going on

)
The main protagonist is a 16 yr HS student named Shinkuro Kurenai who's parents were killed in a very traumatic way while he was still at a young age. He lives alone in a dilapidated apartment and makes ends meet by taking on contracts to settle disputes. This often means violence, broken bones and bloodshed. He may look like a pushover but....
One day, he is asked by his employer to protect a spoiled 7 yo brat who was kidnapped/rescued from her mysterious, depraved and ridiculously wealthy family.
The episodes start off very slice-of-life with comedic elements deriving from the interaction between Shinkuro and Murasaki. Murasaki grew up isolated from the real world, raised essentially like a princess so its hilarious how she responds to dealing with regular people and day-to-day life.
The side characters are also extremely interesting and dynamic.
The only criticism I have is for the OP & ED. They suck! But the soundtrack during the actual show is nothing short of brilliant.
10/10 easily.
Watch this anime if you like slice-of-life comedy, intelligent plot/dialogue and occasional badass kung-fu fighting.