Mykonos' new port is located in an area called Tourlos. It is possible to get from the new port to the old port via taxi or bus - if you want to walk, it is about 2 km to Mykonos town. If you want to take a taxi, the collection point on the harbor quay is on the far right, when you look towards the water, while the bus station is located near the wind turbines on the hillside. A small note is that it can be difficult to get a taxi in high season. The port is also used by large cruise ships and ferries.
It is possible to stock up in the city. There is no water on the quay. Diesel and petrol can be supplied by a mini tanker on the harbor quay.