It depends on what kind of drama you like. I feel like many cheesy/cliche dramas i have seen are for younger audiences or in high school setting.
For a good type of cliche dramas i watch japanese adaptations of shoujo mangas - ceki writes every year an article or two about new adaptations and i am sure you will find something that will catch your eye
Then there is the bad type of cliche dramas which i dont really recommend but are cliche/cheesy (in my opinion). Here belong dramas like (some are bit older because i dont watch much of this genre anymore):
Hana Yori Dango (or its adaptations. The latest is Meteor Garden which is now airing)
Coffee Prince
Coffee House
Dream High
Flower Boy Next Door
Flower Boy Ramyun Shop
High School King of Savvy
Lie to Me
Neil's Cantabile/Nodame Cantabile
It Started with a Kiss (or any of its numerous adaptations. I think the latest is thai adaptation called Kiss Me)
The Heirs
To the Beautiful You/Hana Kimi
Youre Beautiful
And an airing c-drama: Accidentally in Love