Athensfan,
the island will be very quiet when you visit so not sure how many of the tourist 'things' will be open. Lesvos is generally regarded as the worlds finest ouzo producer so dont miss a factory tour in Plomari. The dont stint on samples though so best visited on foot. Beware of the deadly Barbayannis Aphrodite label at 48%! If you can find the ancient watermill just outside Kerameia its a real step back in time. The owner speaks no English but produces amazing products like ouzo flavoured pasta. Many of the products sold in the shop are exported world wide and electricity is generated from the stream by a car alternator. Dont expect a factory this is an ancient one man operation. From Molyvos a short trip to the Eftalou hot springs is an eye opener, you wont believe you can actually submerge yourself in water this hot and then run into what feels like an ice cold sea, its good for you ?? You may find some interesting detail on http://www.imagesofgreece.co.uk This couple visited Lesvos recently and covered a great deal in 2 weeks.

If you can find the ancient watermill just outside Kerameia its a real step back in time. The owner speaks no English but produces amazing products like ouzo flavoured pasta.

That's the sort of tips I'm looking for, marvellous!
I should have explained that we live in Greece, so we can get by with the language & would much rather go somewhere like the watermill than many places that are classed as a 'must do/see' in guide books.
Don't worry about Plomari, one of the reasons for that as a base for a few days is the ouzo, I drink various ones all the time, but want to try some in the 'home' of ouzo!
Any favourite eateries? We look for ones that are open all year & cater for the locals rather than tourists, somewhere with no menu, the owner just rattles of a list of what's on offer that day, that sort of thing. Again, these places are usually by word of mouth, not in guide books!

In Molyvos just a few minutes uphill from the main carpark towards Eftalou is a taverna called Alonia. There is no menu and the owner Antonis is a real character, he is the one always wearing a bandana. We were told that he sold the business a couple of years ago but friends tell us he is still there every night and his mother does the cooking. Great atmosphere and frequent live Greek musicians.