Even if a school isn’t world-famous, that doesn’t mean it isn’t a good school. There are so many colleges in the U.S. where you can get a terrific education, and there are many that would love to have a student like you. Plus, for a field like mechanical engineering, it’s really important to have ABET-accreditation. ABET-accreditation is a rigorous standard, so if a school is ABET-accredited in your fields of interest, you know you will get a solid education.
What is it about these schools that interests you? Apart from having very low admission rates (i.e. very high rejection rates), I don’t see too many similarities, apart from geography.
If you like Caltech because it’s a small school that’s very tech-focused, then you may want to consider a place like New Mexico Institute of Mining & Technology. It has about 1200 undergrads, and as an added bonus, it is a WUE school which means you would get a discounted tuition rate as a resident of a western state. Within its Mech E major there are options for robotics, rocketry, airplanes, and other mechanical engineering interests like Baja SAE teams.
If you’re interested in a big state school with big sports, then there are schools like Oregon State or U. of Arizona or Arizona State that some others have mentioned.
If you like the size, architecture, and diversity of programming at Stanford, then Santa Clara could be a more approachable reach school to consider.
If you want a California public that has more of a residential feel, then Cal State - Chico would be a great extremely likely admit, as I don’t believe there are any capacity issues for its majors (except registered nursing, probably), which means you’d have flexibility to explore and change your mind without transferring, even if you choose a popular major like engineering or business.
Anyway, these are some possibilities, but as others have mentioned, we can better help you when you hone in a bit more on what it is you want out of your college experience. Have you visited any colleges yet, even local ones that you may not be thinking about attending? Sharing any impressions and preferences can be helpful to people offering suggestions.