A show that gives you a nostalgic feel, not necessarily old

It'll be great if it has a great story

I'd recommend the Reply series! They're set in the 90's mostly so the nostalgic atmosphere is already given. Also these dramas are very well-executed and have great casts. I think it's the best to watch them in the order they where released (Reply 1997, 1994 then 1988).
I second the Reply series! It's a must.

Hit the Top
Operation Propisal
Although Tunnel is a crime-solving show, its loaded with nostalgia....
Definitely Reply series dramas (the '1988' ver. probably the most but '1997' ver is also fantastic)
Also the movie called Sunny and tv special The Red Teacher
For some reason Age of Youth made me kinda nostalgic as well
pride (Japanese drama) .. i don;t know exactly why , but the first time i watched it , it gave me those feelings of nostalgia