We made our first trip to India two years ago. On the advice of an Indian friend, we signed up for the Palace on Wheels and they took us among the high points throughout Rajasthan and northern India.

From Wikipedia: The train has a 7 nights & 8 days itinerary departs from New Delhi (Day 1), and covers Jaipur (Day 2), Sawai Madhopur and Chittaurgarh (Day 3), Udaipur (Day 4), Jaisalmer (Day 5), Jodhpur (Day 6), Bharatpur and Agra (Day 7), return to New Delhi (Day 8).

Along the way we met some travelers who took tours by coach, and were exhausted trying to see half of what we saw, because they were stuck on buses all day traveling between locations. We travelled while we slept, and after breakfast would head out to a new city.

Not a backpacker experience, but not so insulated you don't get a feel for the cultural and economic differences.