You should start your trip in New Delhi, don't spend too much time there, and head south to the Taj Mahal. From there travel to Jaipur (the Pink City), Jodhpur (the Blue City), Udaipur (the Lake City), and Jaisalmer (the Golden City). You should stop in Pushkar to have a decent meal and a memorable Shabbat.
We hired a private driver for 8 days for about $700, and it takes about 6 hours driving from city to city. The braves and on-a-budget take the trains. Trains are NOT recommended for single women.
A few high-end hotels allowed us to use their kitchen. We cooked eggs, and fish with our pan. Be sure to ask nicely and explain as best you can. Many people there have no idea what a Jewish person is, let alone Kosher rules, but they do want to make you happy. Tip well.
If you like hiking and outdoors. The north is for you. Chabad is not open there year round, check their listing on KWB for updated information.
The South (Goa and the beaches):
Parties, beaches, and history are in the south. This is where the west met India, and there is Jewish history in Cochin that should not be missed. You will find many Israelis relaxing and finding themselves after their army service.
Mumbai is a serious city, it's India's New York. Plenty of traffic, people, and chaos.
What did we miss? Let us know, and help others travel more and be hungry less.
Whilst there are so many sites to visit in India, we found that the most interesting feature is its people. Every colour, shape, religion you can and can't imagine.
Most people are very friendly, curious and welcoming of foreigners, even Jews.
Take your time. The cities are far apart, and things take time in India. Every place will be crowded.
Make sure to have your visa in order ahead of your trip.
India is a very conservative society. Touching a woman in public (even your own wife) may send the message that she is available to anyone.