The darknets are boring. 97% of it is dead links, info smuggling to countries with internet censorship, CP and drug merchants, and boomers bitching about politics.
This is more of a fucking game than a website or anything, but if you want to get that mysterious wild web feeling you could give Worlds.com a try. It's basically a virtual world with the navigation of darknets with it's WorldMarks, as there is no central hub where to share worlds so you have to seek out and ask other players for those. You could think of the worlds themselves as websites, in a 3D room form. And due to both limitations of the world creation tool(s) and overall 90's atmosphere of the game, a lot of them have that eerie old internet aesthetic.
I guess Second Life falls into this as well, if you don't mind the crippling autism
As for actual websites, what >>169, >>170 and >>219 said. Maybe gopher as well.