I graduated from ITT in 1984 with one of their very first bachelor's degrees, in automated manufacturing technology.  I have worked as an engineer since that time, except one period last year when I was laid off for 10 months.
I've made really good money at it, and have been satisfied with my career, for the most part.
 HOWEVER...  
Go to a real university, get a recognized bachelor of science degree.  Have some fun while going to school.  Join a fraternity.  ITT has no school activities, no teams, no...sense of community.
That will become important to you later.  Trust me.  I miss not having a real "alma mater".  And I find myself apologizing for my degree, rather than being proud of it.
I see guys with University degrees networking together to cover each other, kind of like a squad here.  Universities have a support system on campus to help you adjust.  None of that is available at ITT.
It's your call.  Both routes can get you where you want to be--combined with ability, a good attitude, and hard work.
Good luck, and if you have any questions, look me up in the MA as "shubie".  I'll be glad to help.