Many people from South go to Delhi for vacation. Apart from Delhi, other places like Agra and Jaipur are also on their itinerary.
For visiting Jaipur, catch the night train from Delhi. It reaches Jaipur early in the morning at around 4 AM. At Jaipur station itself, you can stay in waiting room. Plenty of rooms are available, and you can easily get one. Book your sightseeing tour with Rajastan Tourism in the railway station. They are open 24 hours.
After taking some rest, you will start on the sight-seeing tour at 9 AM. They take you to all important locations including Najafgarh and Amer. You are back at 7 PM, to catch your return train at around 12 Midnight.
Similarly, the best way to visit Agra is to take the Taj Express from Delhi. It starts at around 7 AM and reaches Agra at around 9:30. At the First platform of the Agra station itself, you can book your sight-seeing tour of Agra by UP Tourism.
This is a good conducted tour in an AC coach, which takes you to all the important places in Agra, including Fatehpur-Sikri. You are given sufficient time in each location, so that you can look at the monuments in detail. (The guide who accompanied us was very good and my kids very much enjoyed his narration. Even after six long years, they remember this guide.)
After visiting all locations, you are dropped at Agra station, to catch the Taj Express to Delhi. Is this not a convenient way to tour Agra and Jaipur, rather than the inconvenience of the buses? Train travel is any day better than bus travel !!