I got back from Greece in January(Greek Islands are GORGEOUS!). For shoes, I packed two pair, a basic pair of Adidas tennis shoes for walking and running, and a pair of Doc Martens for dress and lighter walking.
We hiked up the mountain side to Ancient Thira(mountain trail, not walking up the road) on Santorini, it was 1200 meters from sea level(we started about 25 meters above sea level), to the summit(you can only go to within about 50 meters of the summit). I wore the Adidas tennis shoes that day and had absolutely zero problems with my feet after going up and then back down the mountainside.
Athens was wet, but the tennis shoes worked great for navigating the streets. At night when we went to dinner I opted to wear the Doc Martens, which are water proof and dressier.
You can't go wrong with a good walking based shoe, as most of the challenges you'll face in Europe will be walking oriented. After two weeks in Greece I was glad I had opted to pack a pair of light weight tennis shoes along with my Doc's, it made the trip easier on my feet and stamina.
Good luck and enjoy Greece! I'm dying to go back already.
-Rob