You can consider below names -

1. National Institute of Technology, Tiruchirappalli
2. National Institute of Technology Karnataka, Surathkal
3. National Institute of Technology, Warangal
4. Motilal Nehru National Institute of Technology, Allahabad
5. National Institute of Technology, Calicut
6. Malviya National Institute of Technology, Jaipur
7. Visvesvaraya National Institute of Technology, Nagpur
8. National Institute of Technology, Rourkela.

IITs-
Indian Institute of Technology Bombay (IIT Bombay)
Indian Institute of Technology Delhi (IIT Delhi)
Indian Institute of Technology Kanpur (IIT Kanpur)
Indian Institute of Technology Madras (IIT Madras)
Indian Institute of Technology Roorkee (IIT Roorkee)
Indian Institute of Technology (IIT Guwahati)
Indian School of Mines (ISM)

Hope this helps!!!

Below are the top NITs for mechanical engineering

 

1- National Institute of Technology, Tiruchirappalli

2- National Institute of Technology Karnataka, Surathkal

3- National Institute of Technology, Warangal

4- Motilal Nehru National Institute of Technology, Allahabad

5- National Institute of Technology, Calicut

6- Malviya National Institute of Technology, Jaipur

7-Visvesvaraya National Institute of Technology, Nagpur

 

Below are the top IITs for mechanical engineering

1- Indian Institute of Technology, Delhi (IIT-D)

2- Indian Institute of Technology Bombay, Mumbai (IIT-B)

3- Indian Institute of Technology, Kharagpur (IIT KGP)

4- Indian Institute of Technology, Kanpur (IIT-K)

5- Indian Institute of Technology Madras (IIT-M)

6- Indian Institute of Technology, Roorkee (IIT-R)

7- Indian Institute of Technology BHU (IIT-BHU), Varanasi

 

Good Luck!!

For mechanical, best IIT'S - IIT DELHI, IIT BOMBAY, IIT KHARAGPUR, IIT KANPUR, IIT Madras...
For NIT's - NIT TRICHI, NIT ROURKELLA, NIT KURUKSHETRA, NIT BHOPAL...