I visited Samos two years ago. I knew in advance that it is a big island, so we decided to rent a car to make a tour around the villages. We stayed in Karlovassi, a nice village but a bit far from the action centres of Samos. During our tour, we saw a lot of historical buildings and some well-preserved mansions that drew our attention. You also have plenty of choices in terms of nightlife and food on the island, everywhere and anytime. Good beaches close to Karlovasi are Mikro and Megalo Seitani, Agios Konstantinos and Tsamadou, a bit far from the village.
If you like trekking, you can follow the trail from Karlovassi to the waterfalls of Potami, but only if the day is not very hot because it is a long way. Drive from Karlovassi across the island and go to Ormos Marathokampou for really fresh fish. The travel guide was suggesting to visit the cave of Pythagoras, but we were out of days laying on the beach. Maybe next time!