All the main tourist spots on the map of Kos are concentrated within walking distance of the port: the ruins of the ancient agora, the Hippocratic sycamore, the medieval castle. But most of the nightlife (clubs, bars, discos) is concentrated in New Town - on a map of Kos, check the area north of the port.
In general, the port on a map of Kos with hotels can be used as a starting point - yachts and boats from other resorts arrive here, kilometers of beaches stretch from here, and the best restaurants and cafes are concentrated on the promenades.
The area in the heart of Kos is Old Town, with traditional narrow streets, stores and restaurants. The most popular with tourists are the neighborhoods near the harbor (if you don't know where to stay in Kos, check out the hotels in the area - there are options for every star rating). From this area, you can walk to all the historical sights and the nearest beaches, and you'll always be in the center of the action.
Another area of Kos where it is better to live as a tourist is the suburb of Lambi, 4 kilometers from the center. It is a developed tourist center with a mass of hotels, a good beach and stores. A little farther (10 kilometers from the center) is the area of Psalidi village - many prefer to settle here, near the beaches, and in the Old Town to go on excursions. There are no dangerous areas in Kos - no industrial and working neighborhoods, almost everywhere tourists live here.