No matter what you are driving, scooter, quad or car, if you are the driver, I am sorry, you will not get to look around too much. You better keep ALWAYS your eyes on the road. Wherever you will go you will have to drive in the mountains, the roads are often narrow, curvy and slippery for the melted asphalt. You will never know what is after the next curve, it can be a car stopped, a bunch of goats, a man on a mule.
Do not take me wrong, it is a lot of fun to drive around Naxos, just need high attention and precautions as all Greece road do.
Be very careful when you drive around with a small scooter (80-100cc), they will assure you that it will be fine for two people to go all over the places, and it is true even if a bigger one would be more confortable BUT make sure you keep your tank always full or nearly full if you plan to visit the Southern and Eastern part of the island, expecially if you rent a small scooter. Those have trouble going uphill with such a load of people and will eat up LOT of gasoline on your way back to Vhora as it is always uphill on very steep roads.
I had a very difficult and worrysome time on my way back from Psili Ammos bay as the steep road to go back to Apiranthos made the gasoline level literally fall under my eyes after every curves and I thought I would have been pushing it for a long way to get back to the first gas station.
There are no more gas station after Filoti, make sure you fill up the tank before you start the downhill way to the sea. You will have to go back the same way and it will be long and slow if you are driving one of those small scooter.
Make sure you ask your rental where the gas stations are, they know it and so you can enjoy your visit with less worry. It is far better to leave a lilttle more gas on the tank when you give your scooter back than having to push it forever.
Roads in Naxos are a little bit dangerous for there are not always guardrails and there are a lot of sharp turns. We have sometimes seen old cars or pickups down the slopes and once we saw an accident just happaende on the road to Bellonia Tower. We found partciularly hard the road from Apeiranthos to Mutsouna, so hard that we after a couple of thrilling bending without guardrail and with a bus coming from the opposite way (!!!!!!!!!) we decided to give up and go back!!!
A common problem i have seen all these years in Naxos is taxi drivers trying to make a bigger income on - as they think - silly tourists. All i can do is to inform you what are the "normal" rates these years. The lowest price you will get to pay is 5 Euro and that is for any drive in the city (for the port, airport, hotel, etc.) with or without your suitcases. For the closest to the town beaches (Prokopios, Agia Anna, Plaka) the rates are almost the same, maybe a little higher, but i would recommend to take the bus which passes every 30 minutes. If you take a taxi to go to the villages, nobody can tell what you are going to pay, you will have to agree with the driver before getting in his cab. But again...i would recommend a bus or to rent a car.
While visiting the Cyclades, keep in mind that in instances the only way to get to, from and around an island is by the sea (unless you are on Santorini, Mykonos). Thus be prepared that you might be stuck on one of the islands for more than you were planning to. The Cyclades are worst affected by the meltémi (known to old Greeks as the Etesians or regular annual northern winds). They are especially strong in early spring or late autumn. We were “caught” by one of those winds and couldn't leave for Naxos for couple days in the end of September.
Well, it’s frustrating not to be in control of your trip, but it’s not the end of the world. There are a lot of things you can do while waiting: you still can swim in the sea (if you are a decent swimmer), go to explore the part of the islands you haven’t explored yet. If you start feeling pressure, read or recall Odyssey’s journey home - couple days are nothing to 10 years it took him to get to Ithaca :)
On a serious note, if you're heading back to Athens to catch a flight, leave yourself a day or two's leeway. Just in case you are at odds with Poseidon :)
Some areas of Naxos don't have any petrol stations; so, be sure your motorbike has enough fuel before leaving for your excursion.
I think that tourist offices on the island have some maps showing where petrol stations are.
As your driving from Agia Anna, south towards Mikri Vigla, you have to use some dirt roads. I was on a motorcycle, and took a nasty spill while coming around a corner. I almost hit a local in a car. He seemed more upset with me, than concerned about my safety, but I guess he has to deal with stupid tourists everyday. A bike is a great way to see the island and beaches, but you really need to be careful on the dirt roads.
When walking around the countryside in Naxos beware of all the spiders and their webs which cross the paths all over the place.
Our faces got covered with webs a lot until we invented a tool to prevent them (see pic.).
If you arrive on a Greek Island outside the main high season (July, August) I would advice you not to deal with the touts at the harbour.
You might get lucky but my experience it is more often a disappointment. Besides, finding accommodation is really easy, at least in June. Just store your luggage (there is always a luggage storage somewhere near, some even free) and take a short walk around town. There are plenty of "rooms to let" signs and you can see it with your own eyes.