India

Mentioned below are the top 20 deemed engineering universities in India
1. Gandhi Institute of Technology and Management Visakhapatnam
2. K L University Vijayawada
3. Sri Sathya Sai University Puttaparthi
4. Vignan University Guntur
5. North Eastern Regional Institute of Science and Technology Itanagar
6. PEC University of Technology Chandigarh
7. Lingaya's University Faridabad
8. Maharishi Markandeshwar University, Mullana Ambala
9. Manav Rachna International University Faridabad
10. Birla Institute of Technology, Mesra Ranchi
11. Indian School of Mines Dhanbad
12. International Institute of Information Technology, Bangalore
13. KLE Academy of Higher Education & Research Belgaum
14. Manipal University Manipal
15. Indian Institute of Space Science and Technology Thiruvananthapuram
16. Bharati Vidyapeeth Pune
17. Institute of Chemical Technology Mumbai
18. KIIT University Bhubaneswar
19. Siksha 'O' Anusandhan Bhubaneswar
20. Sant Longowal Institute of Engineering and Technology Sangrur

I would say take up Lady Shri Ram. I have a friend who studied humanities in Lady Shri Ram, and frequently interacted with students from Ramjas. And there is a major difference between these two.
Lady Shri Ram has an advantage- it is located in South Campus, far away from the hustle and bustle of North Campus. A lot of people believe it to be a disadvantage, but I believe for studying History it is an advantage. Why? Because Lady Shri Ram is never directly affected by any rapid or random change in Delhi University. It also has a great library, and sometimes Ramjas students need to ask LSR girls for books which they were unable to find in their own library.
LSR has a great faculty, which concentrates on grooming the individual, making them conscious about history and historical writing. It also has a strong Students Union which organizes a great history fest, Antiquity, has a close interaction with Jawaharlal Nehru University (JNU) School of Social Sciences (which is near LSR) and also has tie-ups with INTACH, Dastangoi, etc.
If you want to feel the discipline, learn History without putting a commercial element to it, then go to LSR. As a woman, LSR is a liberating sphere, it gives you much more than just education. It is also the leading college of the country now, for a reason.
The statistics speak, so do the experience of students. I think you should take these into account while deciding where to study humanities.