ITT Tech is one of the "chain" proprietary, private-for-profit tech/vocational schools that are starting to "branch out" into nursing, since that's where they see the big money. These programs are approved by the state BONs and you can get licensed if you graduate from one, but, because they are not accredited by the organizations that accredit "regular" colleges and universities, the credits you earn there probably will not transfer into any other schools if you wish to continue your education later on. While you may be thinking now that all you want to be is a bedside staff nurse for the rest of your career, many people started out in nursing thinking that and, a few years later, things looked v. different to them. Once you start working in nursing, you see all kinds of interesting career tracks and opportunities that require more education than an ADN. It's extremely common in nursing for people to return to school to expand their career opportunities. If the credits from your original licensure nursing program are not transferable, you will basically have to start over from scratch if you want to go further in nursing. Nowadays, in nursing, I can't imagine paying tuition for credits and coursework that are not easily transferable to other schools.
Also, in general, these schools are much, much more expensive than comparable programs at community colleges. They are basically charging you (through the nose!) for the convenience of not having to wait or compete to get into the program. A recent thread I saw about the ADN program at a similar school in FL said that that school charges over $41,000 tuition for an ADN program. That is ridiculously, obscenely expensive for an associate's degree, IMHO -- that is more than the cost of an MSN at an Ivy League university!
I'm not in a position to say that anyone definitely shouldn't go to one of these schools, but I would certainly not encourage it. Please look carefully at all your options before making a final decision.