Lesvos is a huge island. You need at least two weeks to see all of it. A lot of beaches and even more small villages. The best villages on Lesvos are found on the coastside, in contrast to Chios where you find the best villages in the mainland. Apart from Mytilini, I also loved Kaloni. Many old houses would sometimes spoil the atmosphere, but the waterfront was great. I miss those hours when we were sitting to eat fresh fish at the numerous taverns along the waterfront, after a whole day in the sun. These were the best moments of our holidays. Do not forget that Kaloni is famous for its great fish. Also buy a traditional textile from the local gift shops and give it a present to your grandma, she will love it.