You will easily find cafes with Internet access in all cities in Austria. Dedicated Internet cafés have become fewer as normal cafés and fast-food shops also offer Internet access. Starbucks was the pioneer as they were first to equip their cafés with wireless connection, and others have followed. All you need there is to have your laptop WiFi enabled; you might also need to ask for access instructions and a password from staff in some cases. Still, there are lots of places with PCs for Internet access – some even offer international keyboards with all the letters you might need in your language. Fees range from €2-5/hour. If the Internet café is your primary point of web-access, look for discount rates or buy access hours in advance, as this makes them cheaper.
You can also buy additional services like printing, scanning etc. in Internet cafes. You can bring your files on a CD or USB-drive and can edit, print and email them there. Be aware that additional services are generally very expensive.
Warning: Internet cafés are popular targets for thieves and pickpockets particularly in the centre of large cities. Keep an eye on your valuables at all times.