Do you have recommendations for specific places in Greece? To dive and also just to visit?
----WARNING : LONG REPLY AHEAD!-----
Well,for a start, if you want to combine diving and tourism, I may suggest the islands of Kea and Leros. Both are nice Aegean islands with superb diving spots, but are not so overcrowded by tourists like 'top-tier' Mykonos and Santorini islands.
1) In
Kea you can dive on the impressive paddle streamer 'Patris' sunk in 1868 (it sits at a depth of 39 meters/127 feet).
For hypoxic trimix technical diving there are the iconic WWI wrecks of HMHS Brittanic (sunk in 1917 at 120 meters/393 feet) and S/S Burdigala (76 meters/249 feet).
2) The seas around
Leros are virtually an underwater depository of warships and warplanes, relics of the fierce battles between the German, Greek and British navies during 1943 (HRNS 'Queen Olga' a greek destroyer sunk by Luftwaffe at a depth of 28 meters/91 feet) german landing vessels, Heinkel and Arado bombers)
3) If you want to go back in
antiquity, you may visit the underwater museum of
Alonissos (an ancient wreck with its cargo of 3.000 wine amphorae at a depth of 28 meters). Alonissos is not your typical aegean island with whitewashed hamlets, but it boasts of nice beaches, pine forests and the nearby National Marine Park.
4) If you like
caves and caverns, then you can visit the Elephant Cave at Chania, Crete (OW certified). On the other hand, if you are a certified cave diver, there are many choices, as the spectacular 'snowy' Amphitrite's Cave (Paros island),
Sintzi Springs ( fresh water cave, mountainous Arcadia, central Peloponesse)
and Vouliagmeni Cave (Athens).
5) If you are just a passer-by for a few days, there some nice diving spots
around Athens: 'KYRA LENI' wreck,
the aforementioned Vouliagmeni cave (for certified cave divers, only!) Legrena (abundance of marine life) Devil's Well of Vouliagmeni
Prophitis Elias, Arzinta's Canyon, Pothitos Reef, and many others that I cannot remember right now.
Sorry for the long post. As for me, a lonesome cowboy somewhere in SW Greece, my sanctuary and diving home is Proti Island, its WWII wreck and its walls. Hope to see you there someday and dive together!