I just did a looooong answer to this & then lost it! GRRRRR!
First of all when are you coming? It makes a difference as to where is busy/busier.
I suggest the Peloponnese for diversity, sites, scenery, beaches, mountains, everything really, & easily accessible from Athens airport.
Some photos of the south west Peloponnese, Koroni, Methoni, Pylos, Chrani, Finikounda, Polilimnio, Voidakilia bay, Gialova, Ancient Messene etc,
http://www.flickr.com/photos/yiassas/collections/72157624647870023/
The north east Peloponnese has Nafplion, a village nearby to base your self might be an idea, there is Epidavros, Mycena, Ancient Corinth, Nemea, Tyrins & the Corinth Canal to explore from here.
North west has Olympia, Kalavryta rack & pinnion railway & the Louisios Gorge, then there's the middle 2 'fingers, The Mani that has it's own history & landscape, Monemvassia on the coast of the other finger, then one of the most scenic drives is across the Langada Pass (Kalamata-Sparti), with the site of Mystras to visit near Sparti.
Islands, well there's so many, but just a couple to consider first are Lesvos, low key tourism there, only a few small 'resorts', very diverse landscape & scenery,
http://www.flickr.com/photos/yiassas/collections/72157625192196112/
Naxos, a lovely island, with the opportunity to visit others from there, such as Paros, Mykonos (commercial & expensive, but worth a day trip!), Delos as well as a trip to a couple of the smaller islands.
Naxos,
http://www.flickr.com/photos/yiassas/sets/72157619603448627/
Mykonos,
http://www.flickr.com/photos/yiassas/sets/72157619613788431/
Delos,
http://www.flickr.com/photos/yiassas/sets/72157619680138310/
There are many other choices too, but I'll wait until you say when you are planning on coming, also whether you'll explore much, sites, history, walking? Once you've started having any ideas of what suits you then I will help with travel logistics, I go to all these places from Athens. Also, do consider some time in Athens itself, I have been about 15 times & not seen it all yet, off there again on Friday!
Here's just a few of my Athens photos,
http://www.flickr.com/photos/yiassas/collections/72157623227125128/
http://www.flickr.com/photos/yiassas/sets/72157625191256604/
http://www.flickr.com/photos/yiassas/sets/72157625067224513/

Athensfan has pretty much got this right. We have had many holidays of the type you are looking for including 6 weeks touring the Peloponesse. We would also suggest Lesvos if you fancy a large mainly non touristy island with Chios accessable by car ferry. The Epirus region would also fit the bill and you could base yourself on Lefkas or further north in Parga or Sivota. Parga is very touristy but also very pretty & charming.

Thank you for your brilliant informative answers. We have so much to consider now. After looking quickly at the places suggested we are leaning towards either South West Poloponnese area, Lesvos or Lefkas. We are thinking of visiting early July before the schools are out on holiday Jill and Dave

I imagine you only have 2 weeks so it wont be possible to cover every thing. Parts of the Peloponesse are very mountainous and have ski resorts so short distances on the map can take longer than you think. Some of the finest beaches in Greece are on the tiny island of Elafonisos just a short ferry ride (with car) off the south coast. An evening spent in a taverna on Monemvasia is also quite unique. The north east has Naplion & Epidavros but unless you want to spend many hours in the car probably best saved for another time. As an example it took us 3.5 hours to drive from Tolon to Monemvasia.

Perfect time to come!
The south west Peloponnese is the place I can give you most detail on, I've lived here for over 4 years, love it & still go out exploring!
If you do choose this area there are several ways of getting here. Flight to Athens, then self drive so you can explore on the way, flight direct to Kalamata (usually expensive) then hire a car. Flight to Athens, then Aegean flight to Kalamata. The first choice is probably the best as it gives you so much more freedom & scope.
If you look at packages try Manos (Thomas Cook), they fly to Kalamata & have properties in Stoupa, Agios Nikolaos & Finikounda, also they may feature Sunrise Hotel again, near Petalidi, excellent location to explore the area. Of these the most commercial is Stoupa, although that is still a lot less than most other places offered as a package!
Sunvil also have a variety of options in the region, Kardamyli, Chrani, Koroni, Gialova & the Sunrise Hotel.
Worth checking these out even if you don't want to use a package, you may find a bargain that beats the flight only price, & don't use the accommodation offered if it doesn't suit, just look for the cheapest package purely as a way of getting here.
For Lesvos the same applies re: checking the flight only versus package, alternatively fly to Athens, connection to Lesvos with Aegean or Olympic, fly back for the last few days in Athens itself.
On Lesvos I would choose several 'bases', we did 3 & managed to see most of the island as you can tell from the photos! Well worth having a Jeep as your car for at least some of the time there as so many of the interesting bits are only accessible by unsurfaced roads.

I'll put in my vote for Lesvos. We went three years ago and had the most blissfully relaxing and enjoyable holiday ever. We stayed at the very un-commercial Hotel Votsala in Pyrgi Thermi. The staff and owners treat you like old friends. They organise outings that take you to some very out-of-the-way places. We were hoping to get back this year but looks like it might be 2012 before we return.