What are the Best graduate universities in US for integrated circuit design and vlsi?

Check ISSCC and see where most of the publications come from. There aren't that many schools in the US offering competitive IC and VLSI ph.d programs.

Top 2:

UC Berkeley

MIT

And the rest:

These schools are arguably about the same. It all depends on the specific research you'd like to do.

- UCLA

- Stanford

- UCSD

- Caltech

- UIUC

- Michigan

- Oregon State University

- UC Irvine

- Cornell University

- UT Austin(for VLSI)