In general, I can tell you that the benefits of a smaller private school like Hopkins will primarily revolve around resources per capita, which allows for early research opportunities, smaller classes, individual attention for academic and career advising and potential networking benefits.
Hopkins R&D expenditures and its heavily military-funded APL create unparalleled opportunities for your future profession. At the same time, though, you’ll see that second behind Hopkins in annual research spending (which one can translate to more numerous and quality undergrad research opportunities and a potential career down the road, in general) is none other than UMich (http://www.bestcolleges.com/features/colleges-with-highest-research-and-development-expenditures/). Notice though that it is nearly a 2:1 difference in spending and nearly 4:1 difference in engineering R&D spending. Nonetheless, while there seems to be plenty of money going around at both schools, also keep in mind Hopkins has about 6000 undergrads (although 15,000 grads as well, most on other campuses) to UMich’s 28,000 undergrads. While this might mean a smaller piece of pie per person in terms of undergrad research opportunities at UMich (and starting early in research is huge if you want to get your name on quality publications and actually learn skills and network in labs), your success more importantly depends on how aggressive you are at seeking those opportunities out, etc. The same goes for advising and educational resources. Hopkins has more resources per person to probably (probably, I don’t know the details on these other schools) provide more individualized attention per student, provide better faculty support, smaller class sizes, etc. But again, if you are a hardworking and active student then you may not need these benefits to reach the same level of success at these larger state schools.
Basically, the higher price tag (and it normally is significant) is buying you more resources if you have questions, need help or want more opportunities. While that sounds nice, that by no means suggests that you can’t work hard on your own and accomplish just as much at UMich/UIUC/UMD, which are all awesome state school. While I admit I’m not familiar with these programs, I am very familiar with UC San Diego and UCLA. Dozens of my friends went for undergrad to these stellar state schools and constantly complained about the difficulties in securing research their freshman or sophomore years (it was very competitive, and even then, sometimes the “research” consisted of grunt work) and complained of non-existent academic and career advising. Given that all three of these schools are large, research focused, and awesome schools makes me think that large stellar state schools will have similar expectations that students need to fend for themselves to a large extent. On the other hand, I sent a single email out to an NIH lab my freshman year and was interning there a month later getting multiple publications over the next four years. Again, this is by no means dooming since many students from UCLA and UCSD are very successful, but it seems to me that they needed to be more self-reliant and hardworking to achieve that success. You definitely should talk to CS students and grads at these schools and get their thoughts on research opportunities (did they start freshman year?), class size, facilities, etc.
When it comes to the sciences, research experience as an undergrad is huge. You are addressing real world problems, learning marketable skills, networking for a potential career and reinforcing what you learn in the classroom. Given that the market is inundated with engineering majors, research experiences (and meaningful ones that ideally involve years in the same lab doing quality stuff) are key to distinguishing yourself and getting a quality job out of college (less of a concern for you in the immediate future, but still vastly beneficial to have meaningful experiences). Hopkins is America’s first research university, and it has maintained its founding vision. It heavily emphasizes, often requires, research experiences for its students, and even encourages independent research with 46 annual $2,500 PURA research grants that you can qualify for even as a freshman. Not very many schools give out $2,500 research grants with limited oversight to unproven freshman based on a small research grant proposal (it is not that competitive or difficult, honestly). Hopkins does put its money (your money?) where its mouth is. http://web.jhu.edu/administration/provost/awards/pura/index.html. I know Hopkins also provides $10,000 Woodrow Wilson Fellowships and $3,000 DURA research grants to its Arts and Sciences students, but I’m unfamiliar with what other grants undergrad Engineering majors can apply for. Nonetheless, it goes to show that Hopkins is committed to the undergrad research experience.
I wouldn’t get too hung up on rankings since (and I’m assuming you’re referencing US News) these program rankings are solely based on surveys sent out to “peers” in the CS field, which includes department heads, faculty, etc. This undoubtedly does have value, but I wouldn’t say that #1 is necessarily better than #10 just based on this ranking approach. Notice here that only 18% of people receiving the CS ranking survey even replied, and you should be wary of findings based on people’s opinion, that’s hardly the strongest metric of performance. Was this ranking survey delivered a week after a mass-mailing by MIT was sent out or a big publication by Stanford came out? People can be easily influenced and often irrational, even PhDs. http://www.usnews.com/education/best-graduate-schools/articles/science-schools-methodology
Driving to UMd for AFROTC is a bummer, but I wouldn’t consider that a deal breaker. It’s a 45-minute drive that you would need to make once a week (JHU worked it out so you don’t have to go multiple times a week). You would probably need to get a car, otherwise it would take about 2 hours to get there via public transportation. If you do go to JHU, students are always selling vehicles upon graduation, so you should be able to find a reasonable deal. Carpooling to split costs and driving time sounds like a great idea if you decide to do this.