That depends on your purpose of coming to Delhi.
If you are coming for your graduation, you can take a room in Hudson lane/Vijay Nagar/Malka Ganj or Saket/Ghitorni/AIIIMS depending upon your college location (North campus or South campus)
If you are preparing for competitive exams you can live in Mukherjee Nagar or Rajender Nagar depending on institute and the exam you are giving.
Now talking about the rent, there are various categories of rooms which are available- 1BHK,2bhk,3bhk. So if more people live your per head cost would reduce.
Typically a two BHK flat in Mukherjee Nagar will cost you around 10–12k. You can also look for PGs in Delhi if you are not interested in doing the household chores(bringing veg, repairs etc).
Staying in delhi for more than 4 years now as an student, I think the best place to dwell in is Hudson Lane or Indira Vihar which is close to Mukherjee Nagar ( the IAS aspirants hub)! What makes these places suitable for students is the security and availability of all resources a student may need.
Get out at 12 at night and you will find students having tea at a corner. That’s what makes these places happening.
But since most of the students choose these areas, the property dealers and landowners oftwn show monopoly with room rents sometimes too high to afford. But this problem can be tackled once you know the floor rates which is around 6000 in Indian money.