I did my undergrad at Rutgers College, which is of course now part of the School of Arts and Sciences of Rutgers University ;-). But, I've also physically been to the Universities of Indiana and Maine. I don't know anything about the reputations of their respective departments in the STEM field. But, in my opinion, RU and Indiana are generally comparable in terms of reputations as universities and are similar in terms of size and overall available academic, and social opportunities, etc. Maine is far different.
A quick check just showed that USNRW currently ranks RU as #64 and Indiana as #79 among National Universities. But, rankings in this zone are known to be fairly fluid. The schools could easily swap places next year. Indiana impressed me a being more of a traditional "Big Ten" school than RU--very vanilla, midwestern vibe, one big sprawling campus in typical college town, far larger residential greek presence (many large frat and sorority houses, etc.). But, most RU students would easily adjust to IU and vice versa.
Each RU and IU are three or four times larger than Maine, ranked much better (Maine's USNWR # is 202) and obviously have far greater financial resources. Academic buildings, dorms, athletic facilities, etc. at UM simply didn't measure-up to what we have or what I saw at IU. UM really comes across more as a large college than a university. And, most SUNY campuses (I'm from NY) are far more cosmopolitan. This doesn't mean that UM isn't a great school. It just makes do with less and lacks a research university vibe present at each RU and IU
My advice, when making her decision, this kid should remember that regardless of the school, the vast majority of her fellow students will be from the state where the university is located and the school's reputation and connections will be more important in that state than in any other state. IU is more relevant in Indiana, just as Rutgers is more relevant in New Jersey, etc.
Also, FWIW, it just seems unlikely that IU would offer an out-of-state student, even a legacy, an academic scholarship (she won't qualify for need-based aid) that would match Rutgers' instate tuition, as it would be worth around $20K a year. In this regard, if this kid is such a stellar student, she should be able to qualify for some sort of academic award at RU, as well, which would definitively render RU the more affordable option. And, with RU, you also avoid another $3-5K, or so, annually in incidental costs associated with having your kid attend an institution that's ~12-hours from home (ask any parent who pays to fly his kid home for Thanksgiving).
Assuming an RU degree could easily be, at least, $50K cheaper for this kid than a diploma from IU and the two schools have comparable rankings and atmospheres, I'd easily pick RU in the absence of some sort of specific reason (like an amazing bio department at IU, etc.). For me, Maine wouldn't even enter into the equation--it's a college that calls itself a university. Just my two cents.