Lesvos is a very big island and you have so many things to see that a week is not enough. We didn't have the chance to see most of the beaches and buses are not that helpful. We spent our week on Molyvos and focused to explore the close area, so we missed nice spots on the sourthern side, like Plomari and Vatera. Anyway, what we managed to see was nice. Beaches of Molyvos and Petra was wonderful, a bit pebbled but very clean. Molivos has excellent fish taverns and locals welcome you. I asked the hotel owner to book us a car for a couple of days and he did found us a car in very good price (50 euros for three days!). So, we explored a bit the area.
The Petrified Forest (close to Sigri) was a bit disappointing. We arrived there in the afternoon and it was closed. We saw a bit from the fence but didn't seem to us so gorgeous as we expected it. Village Mandamados was also nice. We run on it by chance, when we got lost on our way from Mytilini to Molivos and it looked very traditional to me, although I hadn't noticed it in any advertisement. Also go to Eresos to swim and to Kaloni to try fish. They say that Kaloni has the best fish in Lesvos.