The taxi rank and bus stop by the quayside and this is a good starting point to reach the beach of your choice. Bus services are regular and fairly good and operate along the coastal road; a link for the time table here..
Also available for hire are runabout boats from Panormos beach, equipped with outboard motors, ideal for exploring a long coastline, not readily accessible on foot, where are some beautiful, deserted coves; even the inhabited islet of Saint George, tucked in between Skopelos and Alonnissos. There is no more peaceful way of spending a day, than by taking a picnic lunch to your own private beach and share it with the seagulls.
You can fly from Gatwick, Birmingham, Bournemouth, Manchester with
Loloflights.com Manchester & Bournemouth
Easyjet.com Gatwick & Manchester
ThomasCook.com, flyTui.com and others
Hotels look at http://www.skopelostravel.net/hotels/ for a good selection and overview