Great idea to ask this type of question, @jaksakpak. You have some great accomplishments! Re UCLA & UC Davis, I would check the UC system to find out which UC’s you might qualify for. If you can get your ACT or SAT score up a bit, that would really help. They have a specific way of calculating GPA, so you may want to talk to your guidance counselor about this: http://admission.universityofcalifornia.edu/freshman/requirements/gpa-requirement/index.html
As you probably know, schools like UCLA and U Michigan are very difficult to get into (GPAs usually above 3.8 and ACT scores 30 and up. Ck out stats for the Class of 2020 at various UCs http://admission.universityofcalifornia.edu/freshman/profiles/index.html
Based on the schools you listed, it looks like you prefer a university with fairly rigorous academics. Is that correct? Enrollment of 5,000+ includes a LOT of schools. Do you want moderately sized private schools, or really big public schools?
Have your parents s/w you about a financial budget $$? Most OOS larger schools cost quite a bit more than UCs and Cal States. While public schools generally do not offer much $ help. You would probably have a good chance at merit aid at some private schools.
@prezbucky made you quite a good list. Univ of Washington would best fit your criteria, and would be what is called a high match, but within reach for you. We visited last summer, with S17, and thought it was beautiful campus, as well. Other large schools that are in cities: U of Minnesota Twin Cities (quite good OOS tuition) and University of Florida might be an option to look at too. UC Boulder is not is a large city, but a beautiful one. These are all top notch public schools that should be in reach for you.
Most good schools located in large cities are private schools. LMU and Pepperdine are close by, if you are in S Calif, to easily ck out a medium-size schools in the LA area. We have friends at some other great schools of this size: Villanova (Philadelphia), Marquette (Milwaukee), DePaul (Chicago) BU and BC (Boston), GWU (DC), Fordham (NYC) and a fav is Texas is TCU (Texas Christian University - don’t be scared off by the name).
Definitely consider taking the ACT again, as you appear to have done best on that test. Lots of schools will take your top scores from various test sittings, to make a Super Score, so it’s worth giving it another go. Maybe get a tutor to help you with your weaker sections, as you clearly are aiming fairly high. A 28 is a very good score, but If you think you can study and get closer to a 30+, that would be a real bonus to your applications. As a former Californian, whose been happily transplanted to the Midwest, for 20 years, I applaud your effort to find schools outside our lovely home state! 