Well, not be cheeky and judge, Andros has nothing to keep you in Gavrio where your ship will reach first. Just go straight to Batsi where all summer visitors are gathered. But I did not like the beach there because the water is too shallow, suitable I guess for small children!
Stenies is a fascinating all-green mountainous village with a tower to see and pose for souvenir photos. Apikia and the springs of Sariza are outside this village. Follow the path that leads to Pythara, a biotope with streams, lakes and small waterfalls, drowned to dense flora. And if this is not enough for your nature expectations, try the tramp of 7 km approximately through the Dipotamon canyon with the watermills.
I think
Andros has something artistic with all the art exhibitions, wood-carved signs painted in the hand outsdie the shops and with the beautiful museums. Not too far from the port of Rafina(aprox 2 hours) close to Athens but a little bit expensive though!