While there will be “research opportunities” at any school, they will vary by school and department.
How should one define “high quality”? Let’s take the example of a biology LAC professor who rarely publishes. Your kid works with them for 4 years and gets tons of 1-on-1 time. Kid presents their work at campus research fairs and at regional undergrad-only conferences and gets to put that on their CV. Prof writes a stellar letter.
Kid goes to huge public R1 instead. Amazing research with high-profile professors all over the place. Kid competes for a position in a big lab, manages to nab an unpaid 1-year stint, and gets assigned to a PhD student to help with their project. Maybe kid gets authorship on a paper, or gets to present at a conference but probably not. Prof writes a letter but can’t put in many details because she barely knows the kid and there are 3 other lab members named Nick (she gets the Nicks confused).
Or the kid might attend the huge university, apply for a special cohort program, get into a small lab to do paid research in freshman year, get their own project junior year, get 1-on-1 time with the professor, present their work at conferences, and get a stellar detailed letter from the prof (this was my experience at my state flagship).
There’s a lot of possibilities. A highly motivated kid will be able to get research experience no matter where they go. So that wouldn’t be very high on my list of priorities in choosing a school, personally.
The priority is to find a school with a good fit, and then the kid can be really proactive. Do some learning on their own about the professors’ research. Drop by a few professors’ offices to ask them questions about their research, and if they’re looking for students. Apply for NSF REUs starting in the first year (look it up, it’s an amazing program).
There are tradeoffs at big vs small, public vs private, etc. If your kid is leaning toward a LAC, they should not be discouraged thinking that the research opportunities aren’t good enough.
I used to teach at a LAC (now at an R1), and my spouse still teaches at a LAC which is not highly ranked. We and the other profs we know at LACs provide intensive, personalized support for our students to reach their post-graduate goals (and are quite successful). That happens sometimes at big schools, but not nearly as much in my experience. The tradeoff is that the work isn’t as fancy at LACs and gets published less often, but that’s not so important for undergrads.