You want to be going through some of the really long Japanese romance VN's. A lot of those have a long common route that's heavy on the story then you pick a girl and follow that to her ending.
The Majikoi series is a good one to start with. Decent MC, great girls and the story is pretty good with some nice comedy sprinkled in to keep it lighthearted.
Other than that there are games like Oathbreaker, When the Night Comes and recently Your Story that are heavily story based but have romance options that you pick and build up as the story progresses.
No grind in either of those, they are story based VN's where you play through and pick choices.
For western games there are games like Bad Memories, Heavy Five, Retrieving the Past, Alison Fall of the Apple, The Shrink, Becoming and Rockstar, The Author, Reluctant Archon City of Broken Dreamers, Depraved Awakening and Avalon.
There are probably a lot more, just a case of broadening your horizons.
