Jaipur/Ajmer/Pushkar/Udaipur/ Jaisalmer/Bikaner any of these in Rajasthan can be done in two nights. There are overnight trains available from various Delhi stations. It would be hot if you are planning to travel at this time.
Alternatively you can travel to Himachal/Uttarakhand - Shimla/Chail/Dhanulti for the summer season. Be aware of the School holiday season as most of the people rush to mountains.
Agra,Fatehpur Sikri - travel time 3 to 4 hrs
Mathura,Vrindavan - travel time 3 to 4 hrs
Neemrana - travel time 3 hrs
Dehradun,Rishikesh - travel time 6-7 hrs
Nainital - travel time is 6-8 hrs