IIIT

In my honest opinion, out of the choices you've mentioned, IIIT Sri City is the best to go for and there are reasons to support this.
The first and foremost aspect that puts IIIT-S ahead of other colleges is research. The college believes in conducting research programmes that are developmental in nature and provide maximum contribution to the different fields of technology and human nature.
The second factor is the curriculum. We follow a curriculum that is modeled on the curriculum of IIIT-H.
But regarding all other as suggested above, I do not agree. I have crossed over one and highly impressed as I find it as trying to follow and compete with VIT-Vellore and Galgotias in terms of:
(a) Implementation of modern educational concepts and associated internationally renowned faculty from IITs and abroad
(b) Global connectivity by signing MOUs with many renowned technical universities/institutions of USA, UK, Russia and Thailand.
(c) Flexibility for choosing additional courses over RTU, Kota, faculty members, class, class-timing and peers groups of learning.

IIIT Pune and IIIT Nagpur are one among the 20 newly established IIITs.
Being a first batch student of IIIT Srirangam, I can say that the best benefit of being a part of a newly established and reputed IIIT is that the one joining this college will be the seniormost student of the college. Thus, majority of future decisions can be taken by you. In other word, you will be the one to decide how the college will be in future.
As far I know, IIIT Pune will be commencing its first batch in College of Engineering, Pune, which is among the colleges offering good education and placements.
IIIT Nagpur will be commencing its journey from VNIT Nagpur, which is one among the top NITs. So, theres no need of saying how good its going to be.
If asked, I would personally recommend fill IIIT Nagpur ahead of IIIT Pune. However, Pune is an IT hub, so, decisions should be taken smartly.
If compared with local colleges, I would blindly suggest you to join IIITs. IIIT has got a brand name, and it will not take much time to be on the top, ahead of other local colleges.