Hostel Belgrade eye
Probably the best option in Belgrade.
Backpacking hostel in a very nice building. Garden, communal kitchen, laundry service, cable tv, clean and hot showers, etc...
12 Euros the dorm and 17'50 Euros the double room. more
Internet
Cheap Internet access in the city centre. You can easily see it from a distance thanks to a huge banner. They have many computers so it's unlikely you'll have to wait. more