I had to make a very similar decision (Duke, GT, and Caltech) and while I may not be International, I would like to share why I would say to choose GT (as an out-of-state student to each school as well). Yes Caltech has the name, but the emphasis there is a lot more on team-based activities and research than on what you want: an environment to pursue entrepreneurialism. Georgia Tech and UMich are inherently designed (GT more so but UMich still qualifies) to develop students to work in industry. GT has the inVenture prize: the “Nation’s largest undergraduate invention competition” that is designed to provide funding to people with innovative ideas. There is also a large startup culture on campus with plenty of organizations designed solely to aid in getting started in the industry as well as a pretty well-equipped “Invention Studio” with high-end technology and great staff to assist in product development (I personally have designed and 3D printed a lot of things in there as an Aerospace Engineering major and it is pretty incredible).
There is also a VERY good and extensive study abroad program that definitely trumps Caltech’s and slightly edges out UMich’s. Just this summer alone around 80% of my friends are either intern-ing in China, studying in Japan, touring South America, volunteering throughout Africa, or of course studying at GT-Lorraine, to name a few (we also have satellite campuses in China, Singapore, and Ireland btw). About 40% of undergraduates study abroad and there is also a large international community there (Source: many of my friends are international) so you shouldn’t have a problem fitting in.
With large class sizes also don’t worry too much. It ultimately comes down to your preference, but personally I find it easier to stand out in a large school since you are not going to be overshadowed by being in a class full of highly-motivated, bright people like you would at Caltech (not to say UMich or GT students are not smart, but being public means there are plenty of “non-geniuses” in those schools as well). Safety-wise, Atlanta is not the safest at night, but there are PLENTY of transportation options 24/7 as well as emergency phones literally every 15 feet on campus to call the police. I do agree with you about subject diversity though. Unfortunately I think only UMich would provide you with good programs in both the liberal arts and engineering. However if you value a higher tier engineering degree over the presence of good liberal arts programs (and GT has decent ones in that category too. Again it is super industry/international-focused so the language programs are great), then I’d say Caltech or GT.
Source: Second Year Aerospace Engineering Major and International Affairs Minor, International Plan student (a program that requires acquiring language proficiency in a language of choice – I chose French-- taking “globally-focused coursework” and studying for 27 weeks minimum abroad in a country related to your chosen language)