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.
During our Summer 2014 visit to Greece, purchasing a pre-paid phone package named What's Up from Cosmote was 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 15-Euro pre-paid card. Since we wanted data on our cellphone, we allocated 5 Euro of the prepaid minutes to 500 Mb/Month to data through the What's Up App. The whole process took 15 minutes at the store, and a couple of hours to be activated.
The only glitch occurred when the internet settings did not automatically download to our phone, and when we went back to the store, the technician had no clue how to fix it. A quick search on the Internet revealed the coveted settings and it only took a minute to enter them.
Pre-paid cards for this and other company plans are available in every kiosk in Greece if the original 15 Euro get used.
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. And they can be fairly inexpensive. In the summer of 2014 we paid 5 Euro per month for 500MB of data (plenty for email, navigation trough maps, and moderate internet surfing). You may add data coverage on a 2-month contract, or to a pre-paid package that starts at around 5 euro per month (2014 prices).
All three major mobile companies offer just about the same coverage throughout Greece, and 3G is the norm in major metropolitan areas. 4G or LTE was not available in Athens during our visit in 2014, but 3G was fast enough and ubiquitous enough for our purposes. 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 soon after embarkation. After an hour or so from any port, our cellphones connected only through 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!
We did not try it in a big city on in any area where 3G service is available, so perhaps it would be worth a try if you have some money to burn and only stay in big Greek cities.
If you bring your laptop computer to Greece you will undoubtedly want to connect to the internet so you can check your email, and surf around for information.
I agonized over it, but upon arrival to Greece I found out that there is an easy way to gain internet access without signing up with an ISP. All you need is a "prepaid internet card" which you can purchase from a "Periptero" (the ubiquitous yellow kiosks), and an available phone line you can use for the dial-up connection.
I bought a NetKey card for €10 which allows for 20 hours of connection and after fiddling around for ten minutes with my laptop (a Macintosh PowerBook G4 then, and now a MacBook Pro) I was promptly connected to the internet.
The card provides a username and a password, instructions how to set-up your computer for connection, and directions on how to set-up your computer. On the card you will also find a telephone number for the dial-up connection which you can dial form anywhere in Greece. The telephone charge is an added expense, but you pay a substantially discounted price to connect through the special number provided.
When I bought the prepaid internet card the seller at the periptero showed me several I could choose from. They all provided 20 hours of connection, and of course I chose the one with the lower cost -- the NetKey (www.netkey.gr). The NetKey card is issued by ForthNet, the largest ISP in Greece, and the number your dial is the same for the entire country. A friend of mine bought an internet card from "acn" and had nothing but trouble with it. To make matters worst, the card cost €5.00 more than the ForthNet card, and they charged for the telephone technical support (while ForthNet is Free).
So, if you have a laptop computer with a modem, and access to a live telephone line, head for the nearest yellow kiosk and buy a prepaid internet card (if you don't speak Greek here is what you say: mia proplyromene karta internet). I am not sure what the availability of these cards is in smaller towns, so you might want to get one while you are in Athens or at the airport. The account is not renewable, and once you use the 20 hours you have to buy another one and replace the old username and password with the new one.
You will also need a telephone cable. Many hotels have a telephone jack that would fit in a modem port. Simply unplug it from the telephone and plug it into the modem port of your computer and it will work like a charm. If your hotel has the old telephone outlets, you might need a modular telephone adapter to connect your telephone line to the Greek telephone jack on the wall, but these kind of phone jacks are very rare now in Greece. Nonetheless I keep an adapter and an extra telephone cable in my computer back pack just in case I need them.
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 busies parts of the 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.
Usually 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.
Here is our list of what you need to pack for your trip to Greece