There are plenty of lists of weird websites. This is a different question: not where to go, but what to do. These are activities rather than destinations, and most of them cost nothing and need no account.
Listen to the radio in a country you have never been to
Radio Garden puts every broadcasting station on a spinning globe. Drag to Ulaanbaatar, or rural Portugal, or a small town in Iceland, and hear what is actually on air there right now β adverts, traffic reports, local arguments.
It is the fastest way to feel like the internet is still large. In the weird websites collection.
Get dropped somewhere at random and work out where you are
MapCrunch puts you in a random Street View with no clues. Road markings, plug sockets, licence plates, which side people drive on, the language on a shop sign β all of it is evidence.
It is a genuinely good game and you learn a surprising amount of geography by accident.
Race a friend across Wikipedia
Agree a start article and a target, then get there using only links inside the pages. No search, no back button. First to arrive wins.
Details in the friends list, and why this is so absorbing if you want the theory.
Watch the sea get dark
Scroll slowly downward through Neal.funβs deep sea. Creatures appear at the depth they actually live at. It takes a few minutes and the ending is genuinely affecting, which is not what you expect from scrolling.
Find something that was deliberately hidden
The lost media collection is full of things that were broadcast once and never seen again. People find them β occasionally, years later, because someone taped it in 1997 and finally read the thread.
You can join a search. It is a strange hobby and a genuinely useful one. Background here.
Look at a website exactly as it was in 2001
Put any address into the Wayback Machine, pick a year, and browse it as it stood. Try a company you remember, or your own old site if you had one.
The vintage web collection has the best starting points.
Generate something and send it with no explanation
Open any of our generators, roll once, paste the result into a group chat, say nothing. This is either very funny or the end of a friendship.
Keep going
The full bored list, the rabbit holes, or something at random.