From the Wikipedia page 
This is a list of archives in India, which collect and store historical documents, photographs, and other media.
- National Archives of India - established in Kolkata] as the "Imperial Record Department" in 1891. They provide a list of archive addresses here 
- National Film Archive of India
- National Mission for Manuscripts - established in New Delhi in 2003.
- Bihar State Archives - established in Patna in 1912 as the Civil Secretariat Record Room
- Delhi Archives - established in New Delhi in 1972.
- Goa Archives - established in Panaji on 25 February 1595 by Diogo do Couto (Wikipedia page ) and was called "Torre do Tombo do Estado da India". The oldest record is from the year 1498.
- Himachal Pradesh State Archives - established in 1979.
- Karnataka State Archives
- Kerala State Archives - established in Thiruvanandapuram in 1962
- Maharashtra State Archives - in Mumbai, Pune, Kolhapur and Vidarbha.
- Manipur State Archives - established in Imphal in 1982
- Mizoram State Archives - established in Kohima in 1982.
- Nagaland State Archives - established Kohima in 2012.
- Odisha State Archives
- Rajasthan State Archives - is established in Bikaner.
- Tamil Nadu State Archives - established in 1909 as the Madras record office.
- Directorate of State Archives (West Bengal)