Hey! I just finished watching Just You, the Taiwanese drama, and I loved that there was skinship and actually GOOD kisses in it. So, please if anyone knows of anything that has a lot of skinship, that would be great. 

MARS - Taiwanese drama will have what you're looking for :)
Shan Shan comes to eat has lots of kisses and cuddles, but only half of it is subbed right now.
Down with Love (twdrama; might not be right away, but the OTP is cute as heck and there's a good pay off for the build up) Autumn's Concerto, too.  Fated to Love You (you've seen the twversion, but the kversion has a lot skinship too), Pride, MARS.
The first I Need Romance has a good amount of skinship in it.
Thanks for the recs. I'll check one of these out!
I second Shan Shan Comes to Eat (aka Boss and me), which is now all subbed on viki. For the missing episodes, check here.
This is perhaps the drama I've watched with the most skinship :)
The Witch's Romance ; Ugly Alert