Sir, I have got AI 11644 in AIEEE and my catagary state rank is 253. I am interested in EC first and then Mechanical, Computer science, Electrical, Civil etc. First of all which is the best colleage out of above? Secondly please provide me the best order of choices should I fill up for AIEEE counselling.

You cannot fill up LNMIIT or DAIICT during AIEEE counseling. Both these institutions have their own admission process, though they take admission through AIEEE. And their last date for application is long gone. If you haven't filled up their forms, then you have lost an opportunity, since you would have got both the Institutes at your rank.

Assuming that you have filled up their forms, both of them are better than SVNIT when it comes to IT education. (In general, most IIITs are better than most NITs when it comes to CSE or ECE education.)