I've only watched few older J-Dramas but I loved each one of them and many more are on my PTW list.The one's I loved are:
Pride (sports+romance)
Long vacation (romance)
Aishiteru to ittekure (I cried!!! its so beautiful MUST WATCH)
I can confidently recommend any drama Kimura Takuya is in cause' he's a really great actor and he's been in many amazing dramas.There are others that I know people love hreatly but as I haven't watched them myself I can't really recommend them.But you can start with these!
I actually just submitted an article to the MDL editors today that talks about the 10 highest rated Heisei dramas! Definitely look out for the article :D
In the meantime, I agree that Long Vacation is an absolute must-watch!
If you're looking for a place to get older dramas this site is a good resource https://raredoramas.info/