Hi Neel,
Analog VLSI: Courses are very good in ASU, I would say comparable to the best in US. You can find courses in basic Analog/Digital & RF to some advance and specific topic like nyqyuist ADC, oversampling ADC. Few more very good courses are to be added from next year onwards. faculty whom you can approach for research is very few, but there are good number of adjunct faculty who just come from industry to teach courses.
Research in Analog: Currently most research in Analog is in Power Management of IC (Buck, Boost , Solar power etc)
So, if anyone planning to apply in the field of Analog & Mixed Signal/RF I would strongly recommend to apply at ASU.
Digital VLSI: quantity wise not as much courses compared to other univ., but still a very good place for digital VLSI. Basic Digital System & Circuits, VLSI, Advance VLSI, Advance System design (Verilog), Computer Architecture I/II, Embedded System. and few computer courses. Prof. are very good and renowned, job scenario is also very good. Intel is the major employer. People got into Apple/ARM as well.
Research in Digital: more number of prof. than the analog, recently hired 2-3 prof. As far as I know research includes Embedded systems, Memory design and other topics which I don't know right know, but can let you know after consulting my friends.
Many Analog/Digital companies (Freescale, TI, Intel, Microchip, NXP, Maxim, Qualcomm, ON semi, TE connectivity and other small companies) have thier design centers in Tempe or nearby place which is an additional advantage
I have seen more people getting internship in Analog domain than in Digital but more or less scenario is very good in both the domains. and if you are from NSIT you will manage it easily :) So, if you are thinking to apply at ASU, go ahead.
Do, let me know if you have any other question. And in which domain you are planning to apply? ( Digital or Analog?)