If you have a data plan for your mobile device, chances are your carrier would be happy to charge you data roaming rates while you are in Greece. If your budget is unlimited and your heart can handle the bill when you get back home, this is probably your best option: Leave your data roaming on and surf the internet with impunity.
Purchasing a pre-paid phone package named "What's Up" from Cosmote is an excellent option (no this is not an advertisement).
We paid 5 Euro for a new SIM card (which gave us a new phone number - see more details), and we purchased a 10-Euro pre-paid card at the "Germanos" store which gave us 1000 Mb/Month free data. Install the free What's Up app on your phone to manage the special offers (in Greek only). The whole process takes 15 minutes at the store, and a couple of hours to be activated. You need to present your ID for the purchace and the store will keep a photo copy of it.
Pre-paid minutes for this and other company plans are available in every kiosk in Greece if you need to replenish your available minutes or data.
Other companies, such as Wind and Vodafone have similar deals.
If on the other hand you do mind paying extraordinary charges for surfing the internet on your phone or tablet, you should turn cellular data off.
In Greece your best option would be to confine your Internet experience to the available WiFi spots (see below), but if you do need cellular data for things like navigation and checking your email, your best option would be to buy a SIM card when you arrive in Greece. This will give you a new phone number and a local Greek account that won't rely on any "roaming". Read more about acquiring a Greek mobile phone account.
Once you have your new SIM card installed, you could create a "personal hotspot" if your cellphone supports it. This way you can then connect your computer to the internet through your cellphone. In theory, this would work, but in practice it might give you more headaches. You might be charged extra for creating a personal hotspot, and you would probably use your data allocation very quickly.
Your best option here is to use data connection only through your cellphone, and to confine your internet activity to the absolute essentials. Cellphone companies like Wind.gr, Vodaphone, and Cosmote offer competitive packages to choose from.
All three major mobile companies offer just about the same coverage throughout Greece, and 3G is the norm in most areas. 4G or LTE is available in major metropolitan areas. Data rates become "spotty" as you move farther away from the big cities, and dwindle down to a trickle in rural locations.
Mobile coverage while traveling with ferries is even more spotty. While the coverage maps of all major mobile companies in Greece indicate at least 2G coverage in the open parts of the Aegean and the Ionian seas, our personal experience says differently.
We've seen 3G coverages in the immediate vicinity of all the major ports we've docked with a ferry, and that coverage quickly diminished to EDGE or none, soon after embarkation in many cases (especially as you reach the southern parts of the Aegean between Crete and Santorini). Sometimes the cellular connection would drop to "WMS" which would be appropriate only for use during the most dire emergencies given the high rates of 3.08 € per minute and 10.58 € per MB for data roaming.
We have tried purchasing the expensive USB modems available from the major cellular companies in Greece and the results were extremely disappointing.
Making the modem work was a royal pain and the companies who sell them are not much help. When we did get connected to the internet through sheer determination (and countless hours of fiddling with the machine), the connection speed were so slow even downloading our email hang for hours!
It's only worth the trouble if you plan to be in an area that has at least a 3G signal. But if you have such signal, you can use your own phone as a modem by making it a personal hotspot (after getting a prepaid mobile package as described above).
In the end, if your itinerary around Greece is a short one but you still need access to the internet, your best bet would be finding a hotel that offers either broadband in the room (often at an extra fee), or wireless throughout the building (often at low bandwidth connection due to the distance from the router that usually sits at the reception desk). It used to be rare that hotels would offer internet connection, but now you can expect to find it available even in the smallest of towns.
If a hotel with internet connection is not an option, don't despair. Internet cafes and cafeterias or restaurants with free WiFi can be found by the dozen in every large and small town in Greece. The connections are usually very fast and the prices are very reasonable. Most internet cafes exist in the busiest parts of town and offer both wireless connection and desktop computers. This way you can sit at your table with your own laptop and connect via WiFi, or you can use one of their computers.
Sometimes the waiter (or attendant) would simply time your session from the moment he/she gives you the username and password for access and you pay at the end. Other times the sessions are timed automatically through the computer software. In several establishments they even let me connect my own MacBook Pro to their ethernet wire which they would unplug from one of their computer if they didn't have WiFi, so if you are in need it doesn't hurt to ask.
If you travel with computes and cellphones, you probably need cables and some knowledge of the electricla requirements in Greece, so visit is our list of what you need to pack for your trip to Greece