good dramas or movie with strong Bromance?

The dramas with a bromance theme I have seen is school 2013, Shut up flower boy band, Sungkyunkwan scandal, I Am sorry I Love you, I remember you, Rooftop prince, Flower boy next door, She was pretty, Kill me Heal me, Sassy go go, reply 1997.

Warrior Baek Dong Soo

Sassy Go Go has a really strong bromance in it, and so cute! Also has romance too though, so I don't know if that's what you'd be interested in.
Others are
Bromance
School 2013
I Remember You
Shut Up Flower Boy Band (one of my absolute faves!)
Reply 1997

Off the top of my head (all are J-dramas unless otherwise noted):

Battery
*Beach Boys
*Ikebukuro West Gate Park (though it gets dark at times and since OP doesn't like violence/fighting, probably not for them)
*pretty much any Kamen Rider series (some *cough*W*cough* border on straight-up romance rather than "bromance")
*Kisarazu Cat's Eye
*Mahoro Ekimae Bangaichi
Nobuta wo Produce (though I see the OP has already seen this one)
*Ping Pong (J-movie)
Samurai Sensei
*Stand Up!!
*Tiger & Dragon
Tumbling
*Water Boys
Youkai Ningen Bem

(though I like all these-- I wouldn't recommend them otherwise-- the * means it's an especially-loved title)

(J-dramas)
Fuben na Benriya
Tiger & Dragon
Tokubou 

A Gentleman's Dignity - it's a must watch for bromance lover :) beside the romance between the male lead and the leading lady it's all about friendship of 4 men, watching those four in action made me cry from laughing...

The Bridal Mask - very complicated relationship between two friends and those two had more chemistry than the "main couple"

Bad Guys - it's about the most dangerous criminals who are after other criminals, the relationship between those three "bad guys" is very interesting and it develops well during the show

watch these 3 FOR SURE it's about bromance between invloving real brothers/siblings <3

East of Eden

Wakamonotachi

Brotherhood of war