Hey Patricia, I'm 23 and spent almost 2 weeks in Greece this past summer on my own. I visited Athens, Mykonos, and Santorini. I went Mid-May so it wasn't too busy. I have traveled alot through Europe now and find Greece one of my favorite places! I thought Athens was alot safer than many say, much safe than Rome. Still take percautions, money belt ect.
Almost everyone speaks english and found the greek people extremly friendly especially on the islands. If you get a chance fly with Aegean Airlines to at least Santorini, making sure to see Oia, it was stunning, and I am sure no matter what time of year you go it will be beautiful.
I stayed at Athen's Backpackers and had a great time, the hostel is great for single travelers met lots of other cool people I still keep in touch with. The hostel has a roof top bar which is great for meeting people and has an amazing view of the acropolis. While I don't normally stay at "party" hostels this one was fun but not over the top (still got a good nights sleep!)
I didn't stay there but have heard wonderful things about www.hotelantonia.gr on Santorini. There is no hostel in Fira the fun part of the island, but this hotel is cheap with great reviews! It's only a 20 min. bus ride to Oia on a nice coach bus.
You will have a wonderful time, I loved Greece so much I am already heading back with my parents next May!
Oh if you go to Santorini try a Gyro at one of the small whole in the wall places, its the best 2 euros I have ever spent!