There are lots of good Government and private Universities for Engineering.

You can check all Government and Private college/Universities rank wise below:

Top Engineering Colleges in India

Few are top private universities for Engineering:

VIT University, Vellore
SRM University, Chennai
Thapar University, Patiala
SASTRA University, Thanjavur

You can check private college/universities below:

Top Private Engineering Colleges/Universities in India

Good Luck.