You can see the village and surroundings on photos no. 132 - 144 in this album:
Apollon, or Apollonas as they also name it, is on the all year public bus service schedules.
Apollon has many small and nice tavernas along the seafront and a nice snady beach.
You may read more about the village and what it has to offer on these sites:
June is prior to the peak season, and should be too rather quiet.
Do you have a particular reason for wanting to go to Apollonas? It's out on a limb and not ideal if you're depending on public transport. I think there are only a couple of buses a day even in high season.
Apollonas is small but perfectly formed, we stayed in Naxos town last august and we hired a car and visited three times, Its a pretty little place but i'd advise you to hire a car.
Apollon can make a nice day trip from Naxos Town. If you don't wish to drive, you can take a morning bus there, and an afternoon bus back. You will have enough time for a walk up to the kouros, lunch at a taverna, and a little time on the beach.
One of the thrills of my life was a bus trip over the mountains to Apollon during a violent thunderstorm. No rollercoaster ride has been as terrifying! ;-)
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