It sounds completely ridiculous to recommend a research guide published in 1969, but I've found it to be really useful, so here it is:
D. A. Low, J. C. Iltis and M. D. Wainwright, eds., Government Archives in South Asia: A Guide to National and State Archives in Ceylon, India and Pakistan (London, Cambridge U.P., 1969).
This book is a good starting point for major archives in India. It's obviously out of date in some cases, but it has been helpful as a prompt for asking questions. For instance, I can write a letter stating, "One of my sources indicates that records from the Finance Department, 1810-50 (Pre-Mutiny Series) are housed in the National Archives in Delhi. Do you know if that collection is still held in Delhi? If it has been relocated, could you kindly provide information as to its new location?" Perhaps unsurprisingly, many collections haven't moved around a lot since 1969, and even if they have, knowing the provenance of the collection can might help track it down now.