Hello Pritam,

If you are asking for institute other than IIT's then there are many government and private colleges who provide the best Facility and environment. If you don't want to give the JEE entrance exam then still you lot more option to sit any entrance exam for the good college of yourself but in India nothing is better than IIT JEE, here I'm listing some popular and good institutes with entrance exam name-

1- Birla Institute of Technology and Science- BITSAT

2- Vellore Institute of Technology- VITEE

3- Jadavpur university- WBJEE

4- Manipal Institute of Technology- MET

You can participate in any of them, and try to score better to get a good college for you with good branch.

Best of Luck!!!