Someone who isn't petty and obnoxious, or rude.  Getting kinda sick of those.  Maybe like the guy from Boss and Me or Love O2O.  Protective guys are a plus.  

Can You Hear My Heart
Love Letter (http://mydramalist.com/980-love-letter-2003)
I'll Give You the Stars and the Moon
Love Through a Millennium
Return of the Cuckoo
Sassy Go Go

romance a subplot:
Golden Pouch
Naked Fireman
Doctors 
Goodbye Mr. Black (but I wouldnt recommend the show) 
On The Way To The Airport
Prince of Wolf (not the most mature, he's a man with child like innocence) 
Sweet Stranger and Me 
The K2 

Will You Be There? 
Evil Minds 
Falling For Do Jeon 
My Love Eun Dong 
The Eccentric Daughter-in-Law 
Angel Eyes

I tried to find those that were mature and sweet from the very beginning of the show, not sure if these would fulfil your criteria :) 
I was mostly wanting male leads who aren't jerks with a heart of gold.  I like banter and love/hate but sometimes I want something a bit sweeter.  
Aww I also search character like Xiao Nai in Love O2O ahaha

But in my opinion:
The K2
Playfull Kiss
49 Days
Good Morning Call (Recommended)
Just You
She Was Pretty
You Who Came From the Star
I can 100% recommend Soratobu Kouhoushitsu in this category, Sorai Daisuke is completely adorable and totally someone I'd date in real life (unlike 80% of male drama leads).
if you have the patience to watch longer dramas then I suggest 
Five Children - 1st male lead never gets angry or petty, 2nd male lead is full of himself in the beginning(he's famous golf player in it) but you'll see a 180 turn around when he embarrasses himself. 3rd one gets angry only once, 4........., 
i liked the 2nd couple better(Sung Hoon+Shin Hye Sun)
Male lead in Orange Days ~ mature, sweet, kind and supportive. 
Twenty Again-he's had a crush on her for 20 years lol