I would; I always take mine (a Toshiba Portege @ 2.9#).  The Asus is fairly inexpensive, and if it is an old Viao, it is too.  They're light weight, easy to carry, and fit in a bag too small to be a laptop, so theft is not likely.  In addition to being handy for email and picture storage, you can store an enormous amount of information in them - hotel addresses, maps, train schedules, etc.  On mine, I also set up an Excel spreadsheet to keep track of expenses and project how much I need to finish the trip.  That's handy when you go to the ATM for the last time.
This might not apply to Greece, but I have found that, in Germany, cybercafes are becoming a rarity, whereas every little family run B&B has a Wifi connecion.  It's handy, at 11:00 at night, when the cybercafes, if there are any, are closed and you can't sleep due to jet lag, to process your pictures and review you train schedules for the next day.