I originally got into and planned to attend AU this fall, but I just got off the USD waitlist and am considering attending it instead. Cost of attendance will be about the same.
Here are some breakdowns/my pros of each:
AmericanU: Top 10 school for International Relations, location(for opportunities such as internships and events), bigger campus, and politically active(though maybe a bit too much).
Univ San Diego: Way better weather, preferable location for outdoor activities, being able to relax/study at the beach, close to family, top school for study abroad programs(I intend to do a semester at least), & academics are pretty good, but IR isn’t a strong suit at usd.
In terms of risking today for tomorrow, AU seems like the obvious decision, but seeing as how I’m going to go to grad school, and can go to dc for summer internships, the advantages seem to hold less weight.
I’d pick AU unless you think you’d be miserable there.
AU is much better, especially for your chosen major. 
My D graduated from AU. She’s the most non-political person in the world and was not bothered in the slightest by AU’s supposed reputation for political activism–was actually pretty oblivious to it. It’s not like dorm and dining hall conversations are dominated by politics, honest. It’s a college, not the West Wing.
Not sure what this means. Every college these days touts study abroad opportunities, and I doubt any one is really superior. Typically a college will give you credit for any reputable program you find, whether sponsored by that college or not. I’ve never heard of anyone being held back from a legit study abroad opportunity by the institution where they matriculate.
To me AU is obviously the better school for your major.
But, I think there is something else going on. Most of your pros for San Diego make it sound like you are from the area and really don’t want to leave home. That is a legitimate reason for picking USD over AU. Lots of people don’t want to go all the way across the country for college. If you really aren’t ready to move to DC then it OK to go to USD.
USD wouldn’t open the same doors open though so you really need to think about your priorities.
UCSD has a decent IR program, particularly if you have an interest in Asian studies. However, it is hard to beat the DC location of American. American is a good school but realize you will be competing for internships with GW and Georgetown students.
^this is NOT UCSD, but the much smaller, much weaker USD - also located in San Diego but no relation to the UC.