There's no need to sleep or eat in Cybersphere; it's safe to assume your character does these mundane things in the downtime where you're not playing them (there generally isn't a need to drink, either, though certain situations may warrant it).
When you are disconnected from the game your character will be unconscious and remain in the room you left them in. Be sure you're somewhere safe before you do so, otherwise you'll be entirely defenseless! Your character will be unconscious from the moment you use the @quit command or otherwise disconnect from the game.
For the truly down and out, certain alleyways contain cardboard boxes within which you can hide yourself safely (although not cleanly). Additionally, the Syndrome and Transient Hotel both offer secure sleeping coffins for free to those who are really in need, though they will charge a fee for those who are better off. Sleeping in the streets or bars of the city will often result in NCCS hauling you off to the vagrant tank, where again you may have to pay a fee to be released. All of these options are temporary, and will not allow you to store any equipment.
Many bars offer sleeping coffins for more permanent rental, and apartment buildings are scattered around the city. See housing for more information.