It is not exaxcly a tourist trap, but I read somewhere on the guidebook about this water tunnel that was supposed to be intersting as an example of ancient aquedoct. It was suppose to be near Melanes Kuoros site. Well, we went looking for it and we walked for half an hour under a killer sun, on a small trail that was 20% rock and 80% goats' sh*t... at that point we decided it could be the most interesting artefact in the world, we had enaugh.
Unique Suggestions: I suggest you to go looking for it only if you are DEEPLY into water tunnels and wearing close shoes, sandals are not much indicate to walk on goat drops.
One of the most popular places in Chora (Naxos main city) is the road facing the port.
You will see that there are a lot of restaurants there. Above all at night, restaurant owners will try to convince you to enter their restaurant, sometimes in an irritating way.
We had a couple of bad experiences: once seated in a restaurant, we waited for 30mins to be served, and we had to leave because nobody was caring about us, and in an other restaurant we had horrible food.
Unique Suggestions: If you really cannot go anywhere else, go to Popi's Grill. Food is tasty, but it is more expensive than advertised on tourist guides and websites.
Fun Alternatives: Be brave and look for other restaurants in the rest of the city.
Most, if not all of the restaurants in Naxos Town, mainly on the main street in the port, are only for tourists. Don't go there. There are so many other great places to eat, if you just wander around a little. The best food is out of town, which means you'll need a car, or scooter. Go to Agia Anna, or Mikri Vigla, or even Agia Prokoios.