Your daughter will be eligible to apply under NRI quota the following is to be fulfilled.
1. One of the parents of the student should be an NRI and should be residing abroad as an NRI.
2. The person who sponsors the student should be a first-degree relation and should be residing abroad as an NRI.
If the above criteria are fulfilled your daughter's application will be considered. The procedure will be generally on a merit basis. But people who studied in languages other than English should get qualified in TOEFL/ IELTS.
There are many good colleges in India. Some of them are.
1. Shri Ram College of Commerce, New Delhi, Website- http://www.srcc.edu/
2.St. Stephens College, New Delhi. Website- http://www.ststephens.edu/
3. Lady Shri Ram College, Delhi, Website- http://www.lsr.edu.in/
4. Miranda House, Located in Delhi University's North Campus, Website- http://www.mirandahouse.ac.in/
5. St. Xavier's College, Kolkata, Website: http://www.sxccal.edu/default.htm
6. Loyola College, Chennai, Website: http://www.loyolacollege.edu/
7. Christ University, Bangalore, Website: http://www.christuniversity.in/
8. Presidency University, Kolkata, Website:http://presiuniv.ac.in/web/
9. Madras Christian College, Chennai, Website: https://www.mcc.edu.in/
10. Hindu College, Delhi, Website: http://www.hinducollege.ac.in/
The details of the above colleges can be obtained by going through their website mentioned above. There are many other colleges.