I would not normally say this for a first time visitor to Greece, but you should fly to Athens because:-
1. Aer Lingus direct flights ,which start 3 May, are under 200 euro inc. luggage, etc
(If you're a single male then no need for luggage - which would only hamper touring. Greece is informal, and Tshirts and shorts are cheap)
2. The weather in greece ,especially Athens, is perfect in May.Ideal for walking, touring, and long days to see everything.
3. Athens is not only Acropolis, the Agora, National museum but the other sights (rather than sites) -the old quarter of Plaka, the many coastal suburbs - and from Athens you can take day trips to Delphi, Myceane, Epidaurus, Corinth.
..plus very close to a few islands like Aegina,Poros, Hydra ,Spetses.
Aegina for example is under an hour from Athens and you'll meet very few tourists compared to the more familiar isles.
indeed ,you can stay on one or more of those islands if you want a bit of quiet after the busy city.
You can go to the more famous touristic islands like Mykonos on any of twenty boats a day leaving the ports of Athens.
4. There are far fewer crowds of tourists -and the prices are much lower in May.
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You don't need a package for any of the above - book the flight and tbook a cheap hotel for the first few days - then decide if you want to stay or explore.
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there is an alternative that involves a bit more of the traditional pacakage holiday...
- take a package holiday flight to ,say, Zakynthos or Crete from one of the tour operators .and you'll see well priced packages in May (prices based per person sharing a room -if you're solo, forget it)
You'll be bored after a few days - and then you take a local flight to Athens and do what i suggest above - and then last two days back to the resort.
Personally, I wouldn't do that suggestion. Its mainly sea,pool, craic.
It depends if you want package holiday companionship at first. Zakynthos would be O.K. pretty island,nice town and above all only two hours by boat to the mainland whence a short bus trip to Olympia and then take the bus to/and from Athens.
be brave and get to Athens...
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I would second lou2's comments on rhodes -fasicnating old town plus lively modern town -but besides Lindos ruins not much else for cultural holiday.