Rajasthan

Delhi, Jaipur (capital city of Rajasthan) and Agra (city of Tajmahal in Uttar Pradesh) is known as one of the 28 tourism triangle recognized by tourism department of India.

Suggested itinerary:
Day 1: Agra. See Taj in full moon. Stay overnight.
Day 2: See Taj at sunrise. Drive to Jaipur. O/N
Day 3: Jaipur. O/N
Day 4: Drive to Jodhpur. O/N in Jodhpur
Day 5: Jodhpur. O/N train to Jaisalmer
Day 6: Jaisalmer. O/N
Day 7: Jaisalmer. Evening/Overnight train to Jodhpur.
Day 8: Continue to Delhi or future destination

Alternatively, you can skip Jaisalmer above and drive from Jodhpur to Udaipur visiting Ranakpur and Kumbhalgarh on the way. That option will work out to be the same overall duration.

You will not be able to see Taj in the night as per your plan. You need to book the tickets in person in advance a day before you want to see Taj in night. It is allowed 2 days before full moon, full moon and 2 days after full moon. Here is a link  of    archaeological survey of  India. http://asi.nic.in/asi_monu_whs_agratajmahal_night.asp

Palace on Wheels (Fairy Queen Train)-World’s Oldest steam engine

• The heritage train is the oldest locomotive in regular operation as per Guiness World Record.
• The train operates from Delhi to Alwar (a district in Rajasthan )
• After Alwar ,the travellers are taken to the Sariska Tiger Reserve for and overnight stay. 
• There is only one AC coach.
• Generally, the Fairy Queen plies on the 2nd and the 4th Saturday between the months of October and March.
• Accommodation arrangements are done at the Heritage hotel Sariska Palace.