If your EFC is roughly at the level of UC costs (i.e. mid-30’s per year), then you don’t want to be looking at OOS publics (i.e. UWisconsin-Madison, UMichigan, Georgia Tech, UNC) - they will not give aid and your costs will be 50K+ There are a few excellent ones that would be less expensive (Minnesota-Twin Cities, U of Utah) and I agree with @Twoin18 that Utah would be a better choice than Oregon. (Great Honors College, great city + nature… and UofO doesn’t have engineering - you’d have to go with Oregon State + Honors College for that. Also, UofU is a WUE school - neither UofO nor OState offers the WUE discount - and Utah also lets students establish residency after the first year, so it’s a terrific financial deal.) UDub is hugely attractive but even with max OOS merit will come in 10-15K over UC.
For the most part, you need to be focusing on private U’s that meet full need; and she stands to be competitive for many of these.
I rarely do the “jump in and market my own kid’s school” thing, but your daughter sounds like a Rice kid. It’s a single flight to Houston from any CA hub. The flexibility among majors is a huge selling point. It’s important, when applying, to identify a major that makes sense in the context of your academic record and EC’s… but within that zone of things that make sense, there are no worries about not being able to switch into any major (except architecture and music, which have additional layers of application process) that you like. My daughter had a friend who started out as a music major and switched into engineering after one semester. There’s no barrier. This is a big deal for multitalented kids who aren’t sure of their path yet.
Socially speaking, Rice is mid-sized - small enough to be personal but big enough to have all the resources and choices you could want. There is no Greek system, but rather a fully-inclusive Residential College system. Each has its own internal governance/leadership. They compete in intramural sports. Each hosts its own signature campus-wide events. This system facilitates intergenerational friendships and peer mentoring in the same way that Greeks would, without the whole rushing aspect.
Academically, STEM is top-notch across the board - very rigorous, but with a good balance of competition/collaboration. (i.e. there are plenty of premeds/etc. gunning for top grades, but the competition isn’t toxic). Research opportunities abound… the MechE Design Kitchen is particularly cool… and there are many opportunities through immense Houston Med Center nearby. Finance-wise, Rice also has a business school that makes a business minor available to undergrads in any major.
That’s probably enough of a pitch, lol.
Also look at UChicago and Northwestern. UChicago has the intellectual intensity and a residential college system like Rice has, but no engineering - not sure if that’s a deal-killer for your d or not. Northwestern has more of the big-college, rah-rah, Greek life, pre-professional vibe - which it sounds like your daughter might enjoy (think USC with snow).
In the “amazing STEM + intellectual intensity but no engineering” category, look at Reed in Portland. It may be too small and quirky for your d, but a visit would make that clear quickly, one way or the other.
Tulane has decent financial aid and merit aid potential (not that you can stack the two - it’s just two different shots at a good deal) and she might love the vibe of both the school and the city. Likewise Vanderbilt, which is more competitive for both admission and merit, but also probably more generous on the need-based side. Run the NPC’s and see.
UMichigan would be amazing, but they only give OOS financial aid to lower-income families than yours, so $$. Michigan State could be worth a look - she could get some great merit there, and the research and mentoring opportunities for Honors College kids are fantastic, and the school spirit and campus life seem like they’d be a fit.
Then there’s the whole universe of east coast private U’s. Forecast for Carnegie Mellon is dim: they don’t meet full need, and Pittsburgh isn’t as easy to get to from CA as the more major east coast hubs. Cornell sounds like potentially a great fit academically and socially, but a slog-and-a-half to get to. But Princeton, Yale, Columbia, Penn, JHU… and especially Duke seems like it could resonate. (Possibly Wake Forest as a slightly-less-reachy choice, if you don’t mind beta-testing their new engineering program. Boston College is newly launching engineering too.)
Stream-of-consciousness signing off Good luck - I’m sure your d will have terrific options!