In a cyberpunk city, what would it realistically look like to go to download your mind onto the internet, or to at least enter the internet by sending your mind into it, Neuromancer-style? How would you describe things like chatrooms, using search engines like Google, hacking and downloading, if they weren't 2D boxes on a screen, but 3D? What might it even feel like?
The human mind is great at finding patterns and making associations. If something is presented to it that is close enough to an experience it already had, it will fill in the gaps. So it will readily identify boundaries that it cannot cross as "walls", etc.
Since you can disconnect (I am assuming one can in your world) whenever you want without having to "travel" back to your starting point, it makes little sense to use travel as a model for the experience. It would more be like you select a tunnel and the fabric of the world around you shifts until your current point is the same as the other end of that tunnel. A chatroom would be a space or opening wherein multiple visitors are aware of each other and can communicate, maybe even chat. A hacker would be someone who can find a door where there should not be one.
Depending on your connection method, there could be a server in between you and the internet that is processing your requests and converting them into content for a VR helmet or such. Perhaps that is the function of all dedicated access points in your world, is to provide a "translation" service where the signals are converted to a VR experience.
Search engines are servers providing a service, so you would essentially be asking a butler to fetch something for you.
Really your question is very open and the "right" answer is a matter of opinion.