I don't know how to design good websites (maybe that was already obvious to you based on your tastes in web design). I am a huge fan of the plain HTML + minimal CSS look: Nat Friedman websites are goated. But that can't be the pinnacle of good web design.
Even though I'm not really sure what is good, I do know some things that I dislike. I really dislike when websites hijack the scroll and do something funky with it. The most annoying one is websites that add the "content floats up/appears when you scroll down" when it's completely unnecessary. Another big one is horizontal scroll. Another common pattern is when the scrolling is "discrete": either the scroll jumps between sections, or the scroll simply makes more content appear on the current section.
All of these things, in my opinion, are deployed in places where they're unnecessary and don't look good and don't make it easy to traverse the website.
Relatedly, it should be easy for me to find what I'm looking for on your website! I really dislike company websites that don't make it clear what they're doing. This is not a point of "visual" design but I think this is a component of design nonetheless.
I do like very flashy interactive design sometimes. This is not a website, but I've seen clips on Twitter of the menus in one of the Persona games and I thought it was really beautiful. I'm not really sure how to translate that to websites.
I also obviously have some aesthetic biases: I love "old technology" looking things, whether that's simple HTML pages or something like the P*DA from Pokemon Colosseum (admittedly that one doesn't look exceptionally beautiful, but there is a charm to it. Anyways I'm only mentioning it because I saw someone's personal website today that kind of reminded me of it).