I haven't watched Grey's Anatomy myself but have heard a lot of buzz around it, especially around 4-5 years back! Now what I know about the show is that it is a romantic medical drama, but in essence it remains a character drama. The show consists of some really strong and well-written characters; you'll have a favorite or two in no time. It is said to have a unique and interesting storylines, amazing actors and actresses and a truly awesome music and good direction. The show is said to teach lessons by bringing out emotions that no other show is able to do.
I really hope to watch it, but it has 17 seasons which might take me an eternity to complete the show. However, I do watch a similar show called This Is Us (it's not a medical drama, it's more like a family dramedy). But similarly, the show features well-rounded characters, a brilliant narrative and some really good soundtrack and transitions.
It's currently running its season 5 and if not Grey's Anatomy, you might want to give This Is Us a shot.