Indiastat provides statistics on India in the following categories at different administrative levels (you can view them online or download into Excel format): Administrative Units, Agriculture, Banks and Financial Institutions, Civil Supplies and Consumer Affairs, Companies, Cooperatives, Crime and Law, Demographics, Economy, Education, Electoral Data, Environment and Pollution, Foreign Trade, Forest and Wildlife, Geographics, Health, Houses and Households, Industries, Insurance, Labour and Workforce, Market Forecast, Media, Meteorological Information, Mines and Minerals, Per Capita Availability, Petroleum, Power, Social and Welfare Schemes, Sports, States and Union Territories, Telecommunication, Tourism, Transport, Urban Areas, Villages.
Statista is another great source for quick, accessible data (analyzed, not raw) on a variety of topics. For example, check out this "dossier" on social media usage in India.