So apparently the only reason in your eyes to go to NUST is that it has got more number of PhDs (which certainly doesn't matter but lets just count it as NUST's only pro) meanwhile the main advantage of FAST is that its just a few kilometers away from home, secondly, its prominent for its CS degree and obviously much better than NUST and thirdly, you ll get a chance to be an internee if you choose fast which is an absolute WIN!Sorry for talking so much.
Never choose a university on the basis of qualification of the faculty, speaking from my experience, i have been with the teachers holding a PhD degree who doesn't even know a single thing about teaching, at the sametime, saw intructors with a Bachelor degree teaching so wonderful. Its always about the method of teaching not the degrees.
lastly, if i were you, i 'd choose FAST anyday. Just dont get into that hostel stuff, its never easy to live in a dorm. Feel lucky, FAST is just few steps away from you, go for it!