India is vast, and many first-time visitors wonder where to start. One strategy is to tour only a small area, for example Rajasthan or the beaches of Goa. But why not use the excellent train network to see a varied cross-section of India, picking one example of each type of place: one big city, one hill station, one or two princely cities in Rajasthan, Agra (for the Taj Mahal) and perhaps Varanasi (the classic Hindu holy city on the Ganges). 

For example, good and varied itineraries could include:

Delhi-(overnight sleeper train)-Varanasi-(overnight sleeper train)-Agra-(daytime train)-Jaipur-(overnight sleeper train)-Jaisalmer-(overnight sleeper train)-Delhi-(daytime train to Kalka for the famous Shimla Toy Train)-Shimla-(Toy Train then daytime or overnight train)-Delhi

Calcutta-(overnight sleeper train to New Jalpaiguri then the famous Darjeeling Toy Train)-Darjeeling-Varanasi-(overnight sleeper train)-Agra-(daytime train)-Jaipur-(overnight sleeper train)-Calcutta

Overnight trains minimise travelling time, even compared to flying (which is not recommended within India, you'll miss so much).  Use www.indianrailwaysreservation.in to find train times and fares, as explained above. Flights in India