Rajasthan
The classic triangle is Jaipur, Jodhpur and Udaipur, each with a distinct character: Jaipur for scale, Jodhpur for the fort above the blue city, and Udaipur for lakes. Jaisalmer adds a desert leg if you have the days.
Kerala
Kerala is usually travelled as a loop: Kochi for heritage and food, Munnar or Thekkady for the hills, and Alleppey or Kumarakom for the backwaters. Five to seven days covers it without rushing.