You can get a taxi from the airport and ask the driver to go to the Athos Palace or Pallini Beach hotel, in the village of Kallithea in Halkidiki. There are lots of taxis in the airport. The duration of the trip is about one hour, depending on the traffic, and the cost is appx. 50-60 EUR.
This method would be ideal if two or three persons could share a taxi. The same method could be used for the return; in this case you may ask the hotel reception for a taxi.
In order to go from the airport to the Halkidiki KTEL bus station, the best way is to get a taxi. The bus terminal in Thessaloniki is at Karakasi 68, Harilaou district. The ride would cost about 10-15 EUR and take appx. 20-30 minutes, depending on the traffic. We do not recommend you use the public intracity transportation for this case, since the connection between the airport and the Halkidiki KTEL bus station is not good.
The summer timetables are most probably valid also for the beginning of September. The destinations which pass in front of the G-Hotels complex are Paliouri, Pefkohori - Hanioti - Polihrono - Kriopigi or Kallithea - Afitos - Nea Fokea - Nea Potidea. Please take note that buses may be somewhat crowded during this period of the year. The cost of the bus ticket is 7 EUR and the trip could take 1-1.5 hours.
The hotel is immediately after the village of Kallithea. Alternatively, you can take a bus for Kassandria; in that case you should get off the bus in the village of Kallithea and then get a local taxi to go to the hotel (cost 1.5-2 EUR), or go even on foot (20-25 minutes walking distance from Kallithea centre).
There are numerous car-hire outlets (including all the major multi-national companies) at the Thessaloniki International Airport. If you plan to spend some more days in Halkidiki for vacations, this would be the most appropriate choice.