Here is the list of some of the yoga classes that i know.I can give the list of classes where disease based yoga is taught,According to Your disease or illness or aliment the asanas and pranyams are given

Kaivalyadham Institute - Santacruz
Ambika Yoga kutir - Thane
Baba Ramdevji's ashram-Haridwar
Keshav Shristi - near Safaala(near thane)

1. Gordhandas Seksaria College of Yoga & Cultural Synthesis.( A sister branch of Kaivalyadham only)

2. Pranava Yoga Dhama, Mysore(by a comparitively new age Yoga guru -Jaykumar)

3. Purna Swasthya Yoga Therapy Center, Mumbai - By Dr.Pragna Patel. This particular institute specializes on the aspect of yoga therapy.

A branch in Kaivalyadhama, Lonavala by Swami Kuvalayananda is dedicated only to Yogic Healthcare. It has done extensive research on Tridosha theory and gives stress to theory of human anatomy and physiology.

4. Morarji Desai National Institute of Yoga, New Delhi. It is one of the most famous and an autonomous institute in India, fully funded by AYUSH. It realises the importance of Yoga as a health science, especially for stress related psycho-somatic diseases. Its area of research is on effectiveness of yogic practices in preventive, promotive and curative aspects.

5. The international center for Yoga education and research (ICYER), and Yoganjali Natyalam, Pondicherry. It is an institute of international reputation and was founded by the famous Guru and Yoga expert Yoga Maharishi Dr. Swami Gitananda Giri Guru Maharaj, who is one the few leading exponents of Ashtanga Yoga in the 20th century. Swami ji was called as the "Father of scientific Yoga".

6. Vivekananda Yoga Anusandhana Sansthana, Bangalore. It has been set up to examine the efficacy of Yoga practices to solve the basic problems of the high tech era. The study here includes Yoga for modern society, medical application of Yoga, using Yoga for stress management, educational and other applications. The basic principle pf research is to bring the benefits of Yoga to everyone in the society.

7. Krishnamacharya Yoga Mandiram-reputed both nationally and internationally. Founded by TKV Desikachar, his method is based on Krishnamacharya's fundamental principle that Yoga must always be adapted to an individual's changing needs for the purpose of deriving maximum therapeutic benefit. The mission of this Mandiram is to heal people through Yoga. It also emphasizes on "Vedavani" to carry forth an ancient tradition. The research here includes rehabilitation of children who r mentally challenged, aasans for the lower back pain, Pranayama and Thermal Biofeedback techniques for stress and high blood pressure, efficacy of Yoga therapy in management of headaches, asthma, schizophrenia, Better Health by Alternative Life Styles(BETHALS), evaluation of Yoga as a therapy for certain ailments.

8. The Yoga Institute, Santacruz, Mumbai - The sessions here helps people who are suffering from various physical and emotional problems.

9. Art of Living Ashram, Near Bangalore by Shri Shri Ravishankar Ji - Another very popular institute internationally, applies various techniques that produces interest in life and improve the inner potential of a person. It provides practical tools to reduce stress and maintain good health.

10. The Yoga study center-by Brahmachari Rudradev(an Iyengar style follower).

11. Yoga Niketan Ashram-founded by Swami Yogeshwaranand Paramahans.

12. Sri Ved Niketan Ashram-Founded by Shri Vishwaguruji Maharaj Yogasamarat, it conducts Hatha yoga and meditation   courses.Other than catering classes on Yoga, it also offers courses on Hindu philosophy

13. Yog-Ganga Centre for Yoga Studies (Its in Dehradun)-founded by Swati and Rajiv Chanchani(a husband and wife team).

14. Maharishi Mahesh Yogi Ayurvedic Centre, Rishikesh. The branches of Maharishi Mahesh Yogi foundation are all over the world-A very renowned name in the field of Yoga internationally.

15. Parmarth Niketan run by Pujya Swami Chidanand Saraswatiji Maharaj.He has many international followers.

16. Swami Dayananda Ashram-though it is a centre for the study of Vedanta and Sanskrit grammar, regular Yoga programs and camps(Iyengar style) are also held throughout the year.

17. Yoga Cure Institute-an Institute of Yoga Therapy, Kolkata-founded by the great Yogi Guru Buddha Bose, imparts a gentle form of Yoga that is energizing, relaxing and self-healing.This school uses well-tested Yoga techniques in therapeutic form to guide persons to overcome stress, improve health and lifestyle, gain flexibility and reverse the ageing process.

18. The Yoga Vidya Dham, Nasik-established by Yogacharya Vishwas Vasant Mandlik.It operates 5 well-equipped Yoga and Naturopathy treatment centers in Maharashtra. Out of these, 3 centers are in Nasik city while one each is in Kolhapur city and Nagar city.People with various physical and mental ailments like asthma, heart diseases, headache, backache, obesity, neck and back spondylitis and sciatica are treated with the help of Yoga, ayurveda and naturopathy treatments.

19. Yoga India (Mysore)-Already mentioned in above posts.

20. Institute of Naturopathy & Yogic Sciences, Bangalore

21. Babaji Kriya Yoga Center, Bangalore

22. Shri Ambika Yog Kutir, Thane(Maharashtra)

Apart from these centers,  few other very famous Gurus/Guru Maa who have their own style of teaching and incorporate few aspects of Yoga. They have discovered some simple techniques for the common man for a stress free life.They may be termed as a spiritual awakening centers(rather than a Yoga center) Few of them are-

23. Sahaja Yoga-By Maa Nirmala Devi Ji

24. Raj Yoga by Brahmakumaris-The main center is at Mt. Abu. They have around 8000 centers all over the world.

25. Osho Commune International, Pune-I don't think this needs any description.

26. Dhyan Foundation, Delhi-by Yogi Ashwini-comparatively a very new age guru who has propounded a technique called asSanatan Kriya, which I personally feel is a mix of Pranic Healing techniques,yoga(some sookshma vyaayaams and praanaayams) and Vedic chanting.

27. Anandmurti GuruMaa Ashram-Gannaur, Distt. Sonepat, Haryana.Another very famous institute in India.I think this also doesn't needs any description.

28. Pujya Sant Sri Asaram Bapu Ashram, Ahmedabad.Iske bhi description ki koi mujhe nahi lagta koi aavashyakta hogi.India mein har koi jaanta hai.

29. Pranic Healing Foundation-It has local chapters in all the major cities of India.

30. Kayakalp, Palampur, Himachal Pradesh-Its more into Panchakarma and Naturopathy.

31. To learn Buddhist techniques of Meditation,one can visit Dharamshala/McLeodGanj-A heavenly abode..!!Though they have centers in other cities also.

These are several institutes to learn yoga in INDIA