Are you travelling alone ? If yes, then my best advice is consult this with your travel agency. You have to arrange everything before you arrived there.
India is a big country, so you have to decided which places or city that you would like to go.
Delhi is the nicest city to visit because there are a lot of interesting places to see. At least it is easier to go to Taj Mahal (Agra) from Delhi. Also there is a legendary Qutab Mnar, Humayun's Tomb, India Gate (a war memorial likes in Paris (triomph de arch..forgotten how to write it), Purana Qila, Safdarjung's Tomb, Lotus Temple.
From Delhi you can go to Agra, without even stay there or if it is near full moon, I would like to advice you to stay 1 night at Agra, so you have a chance to see Taj Mahal at dawn and after that you can visit Agra Fort, Fathepur-Sikri.
Back to Delhi and the next day you can go to Jaipur. I don't have a chance to visit Jaipur, but if I do have a chance to visit India, I'll go to Delhi again and go to Jaipur.
People said if it is summer, April - May - June, it is not a best time to visit India, because of the weather becomes very hot, and if you are not from Asia it will be worst thing.
But please remember, since you are foreigner, they will charged you twice the indian people for every tourist visit and even air plane ticket. Also, please check all the hotel from beginning otherwise you get cheated by the travel agent (be carefull to choose the travel agent, I have bad experience with one of Delhi travel agent recommended by the EPCH).
So if you don't have much time, I would like to suggest you to go to Delhi...there are a lot of interesting places and be the central city to go to Agra and Jaipur.
Enjoy your time in India, it is a beautiful country and even though I have bad experience, I still would like to come back again.