Hi
I fly into Thessaloniki and hire a car and then drive 2 hours to Keramoti and get the ferry to Thassos.
Alternatively you could go to Halkidiki, there are 3 peninsulars Kassandra Sithonia and Athos, I have been to Kassandra and Sithonia and without question Sithonia is the best if you want great beaches and tranquility, Kassandra is imo too commercial.
The drive from The airport to halkidiki is a bout 1.5 hours.

Thessalonika is in Halkidiki.
There are three pennisulas (the three fingers) that stick out at the end .
Kassandra is very popular with a lot of Greeks, English, Russian and Dutch.
Sithonia is less commercial apparently but a lot of people have said there is mainly germans there.
The Third finger is where Mount Athos a men only Monastery is situated, not much else.
Have visited many Kassandra poennisula many times and stayed in Hanioti which is nice, also visiting Pefkohori and Polichrono on my travels.However too be honest they are quite a distance from the Airport , that is all the pennisulas. If you want something a little bit closer you can try the Gerakini beach area or Sani.
Hope you find something.

Actually Thessalonika airport (locally known as makedonia airport) is just above the border for Halkidiki , but serves Halkidiki as it the nearest.

Thessalonika airport (locally known as makedonia airport)

but more commonly called salonika.. found it to be quite good by Greek standards last year

wizard

Galaxias Beach Hotel 4 stars
2, Gr.Lambraki str, 57019 Thessaloniki

http://www.galaxias-hotels.com/

This beach is 9km from the airport. have a look at this link as you dont have to drive far from the city to find beach resorts