• Hindustan Institute of Technology & Science, [HITS] Chennai
• VelTech University, Chennai
• VIT University, [VIT] Vellore
• Bharath University, Chennai
• Karunya University, Coimbatore
• Coimbatore Marine College, [CMC] Coimbatore
• Guru Shree Shanti Vijai Jain College for Women, [GSSVJCW] Chennai
• SRM University, Vadapalani Campus, Chennai

The best colleges which you should have in your list are-

Madras Christian college

Amity global business school

Hindustan Institute of technology and science

Loyola college

Shri Rama Chandra university

The new college

Tamil nadu open university

Hope this helps you.