Xleem

In the end, I believe academic fit ultimately trumps rankings, especially considering lists like US News are not super reliable for an assortment of reasons (and, of course, does not consider individual departmental strengths). Something to consider is the fact that since the POI at the prestigious university is a big name, they might not have as much time to provide individualized attention (senior and/or big-name scholars might teach fewer classes or might not even take on new students). Plus, it would be different if you had several POI at this higher-ranked university--you only mentioned one, and to me, this is suuuuuper risky, because what if that individual retires, goes on sabbatical/leave, or decides to leave that institution in favor of another? Or, in the worst case scenario, what if you don't even like working with that person? What if they turn out to be super unreliable? If you welcome multiple professors to work with, then at the very least you can receive new insights and perspectives. 
Maybe ask the DGS at the prestigious university if they intend to hire any tenure-track with your specialization in the foreseeable future. Maybe even reach out to graduate students about affordability and/or "family-friendliness" in both cities/towns. Question where you can imagine yourself living for 5-7 years while still managing to do research with faculty. Schools with higher endowments and prestige clearly carry a wealth of resources to peruse (sometimes this manifests in higher stipends, more fellowship opportunities, more travel funding for conferences, etc.), but the ability to conduct research in the department with faculty mentors strikes me as equally important. And depending on what other factors you are considering, the pros and cons are limitless. 
I know someone at my current grad seminar who turned down a very prestigious, highly ranked English doctoral program in favor of her current program because the latter was more affordable and hosted multiple tenured faculty in her line of interest, even if her current program is not nearly as well-known. I'm in the same boat and I found this incredibly useful to consider. 

The way I understand it, there is a small but important difference between a "visa" and "status".
 
The "visa" has your photo on it and looks like a passport page. It is also attached to one of the pages in your passport. The "visa" simply allows you to enter the US for some specified reason (e.g. tourism, business, work, school). There are two restrictions on visas usually: time and # of entries. The length of your visa and how many times you may enter the country is dependent on treaties between the US and your home country and does not necessarily reflect the time on your I-20. It doesn't matter if your visa expires during your time in the US -- you don't have to leave if your visa expires. The visa is only used for entering, not staying, in the US.
 
For example, I know some PhD students who only get issued 1-year visas because of their home country even though they are in 5-6 year PhD programs. This is a hassle because this means if they visit home (or even go to an international conference) after their visa expires, they will need to apply for a new visa before they can re-enter. In your case, it seems like you have the opposite case -- your home country gets a 4-year visa with the US even though your program is only 2 years. 
 
"Status" is something like F-1 or J-1 and the proof of your status is not the "visa", but the I-20 or DS-2019 form. The I-20 proves your F-1 status, which is what allows you to actually stay in the US, and apply for a driver's license, social security, etc. Unlike your "visa", you do have to leave the US when your "status" (I-20) expires! 

My understanding of this requirement is that they want to make sure you aren't using your F-1 status to otherwise gain entry to the US. For example, they would not want people to enter the US on F-1 statuses just to meet an American, marry them, and then, for example, quit school and get a green card through marriage. So, they are interested in seeing that, to the best of your current knowledge, you intend to be in the US only to complete your studies and that you intend to return home after you finish your school. They want you to say that you don't have any concrete plans to stay in the US or that you are studying in the US with the express purpose of getting a job in the US. 
 
I had found a document/memo issued by US Immigration about verifying a student's intent, but I can't seem to find it nor my former post on gradcafe about the document. In that document, it explicitly reminds US Immigration officials that students are a special case since we are mostly young so it's hard to show that we have ties in our former country. Unlike a tourist visa, we can't really have a return ticket before the expiry of our status and we might not own property in our home countries. The document also notes that students might not really know what will happen later on. Being on F-1 status does NOT preclude from marrying an American and staying in the US nor does it prevent you from being hired by a US company and end up switching to an immigrant class visa. 
 
They just want you to declare that the sole reason you are seeking a F-1 visa is for the sole purpose of a F-1 visa -- i.e. a chance to study in the US. If you end up staying, that's fine, but they don't want people using F-1 visas (a non-immigrant class visa) as a way to get an immigrant class visa. So, to be safe, I would probably avoid lying about where you're staying, why you've visited in the past, or whether or not you have a SO in the US. Be honest. But there's no need to speculate about the future in a way that might hurt you either. That is, don't say "oh we might get married" or "I hope a US degree will help me get a US job" etc. If asked directly, I would just admit that you are uncertain about the future and for now, your focus is just finishing your degree in the US.