The right direction will always be the cheapest option.

You are right to avoid any place that won't do direct-to-major.  You don't want to risk getting on the wrong side of whatever their gatekeeping criteria is and having to transfer somewhere else to get your arch. degree.

Is it correct to assume that VT is going to be less expensive for you than Parsons?

Yes, Parsons total cost is still more expensive than VT, mainly because of the location (NYC vs Blacksburg, VA).  Thanks a lot.

Most of the undergraduate programs (in a way graduate too) are similar in terms of curriculum and faculty, and mostly in a good way.
For me, the school's context would matter in terms of the school's proximity to a bigger architectural community with its events, lectures, resources, important examples of architecture old and new, and cultural exchanges. Those are going to be useful influences in your development as an architecture student and are not available as a class. If you manage your time well, you can tap into these 'amenities' and get the most out of your school years while trying to shape your future.
But the biggest advice will be to sign into a program that is also within a sustainable budget as it is already mentioned. A lot of things I wrote above are also within your reach through your computer.
+, Blacksburg, VA could be very interesting too. It didn't happen to me but staying out of the urban centers can be a very valuable experience I can imagine. You never know I guess.
Looks like you are about to make the right decision even though I don't know what the 'right decision' is to you.
Architecture education is also about what you make out of what you have in front of you.