Browsers track visits in their history, Firefox for example in a file called "places.sqlite" which you could copy and use as a base log.

If you don't mind a bit of tinkering and are a Linux user, you can start with a squid proxy on your server which will keep a log. That could be a Raspi at home. Your browser can connect to that server, either directly, or via SOCKS5 or even an ssh tunnel if the proxy is running on your (external) server.

These ssh tunnels are very flexible things. I use an ssh tunnel and SOCK5 on top of that so my network cannot be traced by my provider. The tunnel is set up in a terminal window like

  ssh -D 8080 -l user proxy.mydomain.net sleep $[45*60]

and the browser (Firefox for example) is configured to use the proxy at "localhost:8080" which routes its network connection through the tunnel exiting at my server. The "sleep ..." is any command you want to run instead of a real login session, i.e. you can just drop it if you want. One can add a proxy into this chain. Or use "ssh -v -D ..." to get a log where you can extract your destinations.

The AI part would not trivial in general, and especially because of "content creators" and "SEE optimizers" ... and last but not least dynamic web pages.

Edited: clarification and typo removal.