This is very much Work In Progress, more thoughts than a structured guide. YMMV 🙂
It's the name of a concept which many sites align with.
There are similar names which may point to many of the same sites. Cool Web. Old Web, evoking Geocities and MySpace. There is also Cozy Web, but I think that means something different. Indie Web
Where can you go to make a Personal Website? Commercial, free options exist, but the catch is they're proprietary, and they want to keep you there until you pay. There are better options, hosts such as
Let's explore! Neocities websites listing. Nekoweb websites listing. https://marginalia-search.com/explore page
Web rings
Search engines which focus on the less commercial side of the web. https://marginalia-search.com
Here's a special incantation which will point Marginalia mostly to the Personal, Indie, Cool, Awesome Web. Type your search before the additional search terms.