Internet cafés have just begun to really take off in Geneva, and there are now several that stay open fairly late.
Internet Café Cornavin, inside the Cornavin train station near the west entrance. Until 10PM every day. This convenient and friendly place offers printing, and laptop stations. If you do plan to use your laptop you need to be able to demonstrate that you have anti-virus software. 6CHF per hour. (specials for regulars and students).
Point6, 12 rue Jean Violette, +41 22 800 26 00. Primarily a gamer internet cafe, but becoming quite popular with casual internet users. Scanning/photocopying/printing, diskettes/CD burning, faxing services available. Manned by a young staff who as a result of being surrounded by snack machines and video games are very friendly. Prices: free for first five minutes, then 5CHF an hour.
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