Spring is the best season to visit Athens. The weather is neither too cold nor too hot and you can enjoy walking. You will also see many flowers at parks, balconies, squares.
Unfortunately, you cannot get flowers or plants to your country due to international laws, (unless you come from Europe) but you can have with you dried herbs (basil, mint, daphne etc). You can use them when you cook, and you will like them a lot. You can also drink chamomile, local tea, and so on and you will like the way that laventer aromatizes your clothes. Just try. You will find herbs everywhere.
While walking at the historical center you will see pots with flowers in many colors. Greeks like flowers, although there are many empty balconies- as well as balconies that remind you of a garden.
Enjoy the smells and the colors. And shoot everything- with your camera. The combination of nature and ancient ruins is superb, don't forget to visit an archaeological site and admire the whole, beautiful, thing.