Once you've decided on what you plan to drag around Greece with you, you may need some wardrobe items - lightweight underwear, a new swimsuit, shorts, and so on. Don't blow your Greece budget, but get what you need.
This is also a great time to shop for travel gadgets which can make your trip easier - adaptor plugs, voltage converters, maybe a new camera or more memory storage devices for existing ones.
Need someone to watch over things at home? Start bribing the neighbors and then Remind them of those old "Sure I'll watch your house/feed your cat/water your plant while you travel in Greece" commitments. Line up a primary caregiver, a backup provider, and call two or three professionals - and take those numbers with you. This is more crucial for longer trips to Greece, when things can go just wrong enough - or you may extend your trip enough - that previously reliable people may have unexpected events in their own lives which prevent them from helping you. By the way, some travel insurance policies will cover pet care if you're delayed.
If you want to book your own tours and airport transfers, this is a good time to do so if you are confident that your plans are solid.