Tilly said:
Steins; Gate has pretty awesome reviews. Try that!
Yup I would definitely go for this picked it up on a whim for PS3 recently for 20 quid and its one of the best buying decisions I have made for a game in years (piece of Entertainment software would probably be a better description than game).
Strange I have read only tried a few Visual Novels but they have provided fantastic entertaining experiences (with a few duds I dropped) and yet I still have this stigma about them like I am unwilling to spend money on them for some reason.
As I have said I am not really that knowledgeable but I would also strongly recommend Saya No Uta in addition to Steins gate its pretty short especially in comparison and has very few choices but damn what a story.
Of course there is Katawa Shoujo which is free and was the first one I ever read. Its not as good as the above 2 imo but its still definitely worth a look especially for the price it is.
EDIT: If it absolutely has to be a cyberpunk world ignore the above. They are all set in our world or at least a world very similar to ours.