Referring to the serious or more popularly known as 'Art' cinema. Older movies like Saaransh, Ardh Satya, Ankur, etc. I guess not many like to watch such kind, the 'slice of life', stuff. One of my favourite contemporary directors is Vishal Bhardwaj, absolutely love the way he presents his ideas. Also in the league would be Dibankar Banerjee (and Anurag Kashyap), should watch his Khosla Ka Ghosla.
Love this song from one of his movies, you might like it if you haven't heard it yet:
https://www.youtube.com/watch?v=8FMz_KT1mC4
I'll give these movies are try. If you know of any more, do share.
Also, is there a website where people talk about these types of movies with reviews, etc. Most bollywood website just discuss the mainstream movies.