Fantastic views out over Naxos town and to the sea from the 1739 café and from the viewing platform beside it (for which you don't need to visit the café). It's near the top of the Kastro or oldest part of Naxos town but there's an elevator for those not keen on a lot of stairs. The staff are friendly and helpful, the music is gentle and mainly Greek, the tea, coffee and other drinks are really good, the lemon meringue cake was a little too sweet but that's a matter of taste. It's great to get a bottle of tap water in a proper glass bottle instead of in wasteful and nasty plastic, and the prices are really good for such a venue.
The design shop below the cafe is well worth a visit too - it has very high standard pottery and gifts of all sorts - far better than in most of the touristy souvenir shops, and still with reasonable prices.