@PoliSciGuy23
I think what has been said so far is excellent and very representative, at least based on what I know about GMU which is a lot like what @VAmomof4 has said. The other thing I “know” about GMU is that their econ department is pretty strong and tends towards the more conservative, UChicago philosophy of econ. I have heard that the student body tends to run a little more conservative than most as well, but I am far less sure about that.
New Orleans is, indeed, very accessible to students without requiring a car. The streetcar gets you to most of the interesting places you want, and you can bike or bus to other places.
As far as travel there would always be friends traveling to the same place you are, so coordinating flights so that you travel together should be fairly easy (and saves money on the taxi fare). That makes the travel a lot more tolerable. I assume you would be flying in and out of either Newark or Philly, and Tulane draws heavily from both areas.
I want to dispel two notions you seem to have. The first is that Tulane students are “snobby”. I have absolutely, consistently and invariably heard nothing but the opposite for Tulane students in general. Of course any individual student might be a snob, but apparently they are fairly uncommon at Tulane. Parents and students come back from trips to Tulane and virtually always report that the Tulane students were the friendliest and most helpful of any campus they visited, and that they seemed the happiest to be where they were. Tulane students tend to wear Tulane clothing at a higher rate than most other students do of their school. Hardly a scientific finding, but again a consistent observation of people that visit the campus. That says something, I think.
The second notion that I think is incorrect is that because you go to school in or near DC, internship opportunities are higher. I just don’t think that is right. Anyone can apply for those opportunities, and they screen them all the same regardless of location, as long as you are a US citizen. As faithful readers of this forum know, my D (a recent Tulane grad) was selected while still at Tulane to work at the Department of State in DC last summer, and this summer will be back with them, posted in Taipei, Taiwan. I know she also looked at other Federal opportunities such as Congressional situations, and I think with some local political think tanks as well. I am sure there are others. With the reach of the Internet, I think the advantage of being in the DC area is far less than it used to be. Besides, even if I stipulated that there was an advantage, you would be competing with so many more students for those slots like at Georgetown, George Washington, American, and probably Johns Hopkins as well, and a host of other schools in the area I am sure. While at Tulane, you could not only try for those positions, you could also try for local and state positions where I bet preference is given to local schools. Just something to think about, but the main point is she got her position while living in NOLA.
Oh, and I would completely ignore rankings if I were you. They are less than meaningless at the undergraduate level, and suffice it to say I am very sure both schools have departments that are more than capable of providing a complete education in the area.
The great thing for you is that you cannot go wrong academically with either choice. It really comes down to what feels right to you. Listen to your gut. It is usually right.