the hypothetical situation in which SpaceX has partnered with NASA
Instead of hypotheticals, why not look at the work they've already done together?
This 2019 Business Insider article (paywalled, alas, though you can find text-only versions of the article in some less reputable places I shan't link to, just in case) took a look at some of the HiRISE image requests made by a NASA scientist in relation to some work with SpaceX, the precise details of which were under NDA. The current list of locations of interest is here, but the original article included this nice map:
The two big peaks you can see there are Elysium Mons at the left, and Olympus mons at the far right. Most of the regions of interest are in Arcadia Planitia, based on the belief that it will be easiest to obtain water from there, which you'll be needing in order to do stuff like make rocket fuel to travel to and from Earth economically.
There's a secondary benefit about the Arcadia site, which is that it is in a relatively low-lying area of Mars which means that the atmosphere is thicker and so the cosmic radiation dosage is somewhat reduced:
This map doesn't conveniently match up with the google-mars generated image above, but you can just about see Elysium at the upper-right of the left hand hemisphere, and Olympus Mons just left on centre on the right hemisphere.
Whilst there are tradeoffs to be made (thicker atmosphere means more problems from dust storms) there's clearly good reason to be visiting that part of the planet.
As for science... well. Everywhere on Mars will be interesting to some degree... whilst other places might have greater interest, you still need to be able to support scientific investigation of those places, and teleoperation of robots or even visits in person will be vastly easier given a decent base camp to work from, and that'll be the main driver of early manned stuff, I'll bet. Putting boots on Mars will be too difficult and too expensive otherwise.