I think you definitely need a car while staying in Naxos - it's a big island with plenty to see and you'd be short changing yourself not to have a vehicle. The beach near Marios's place is lovely, even though at first we thought it looked rather busy as lots of people drive to visit it. But that's because it really is a lovely beach. In general I would consider getting one of those "tent" sun shades for the Greek island beaches, as in August at least there is lots of wind. Our favourite restaurant was Taverna Axiotissa, the food is delicious and it's reasonably priced with very friendly staff. Marios's restaurant recommendations were pretty reliable. If you can then I would stay at least a week - we were on Naxos for seven nights and felt we could have happily stayed a few days more.