hello luci
so you are visiting napoli....bella napoli. a real pity you do not want to spend your time in the city itself. contrary to popular belief, it is a magnificent city and the home to the worlds first opera house, the worlds first archeological museum, the worlds first aquarium to mention a few. however, as you wish to venture i hope the following will help. from naples you are best taking the jet boat to capri from the "molo beverello" the small harbour next to the main maritime station, i imagine your ship will dock there. there are numerous operators offering transport to capri and you will see all their ticket windows facing the castle. my advise, is go the the waterside and see the "metro del mare" kiosk. these are new and cost a fraction of the normal operators. the "metro del mare" is operated by the campania region.
on capri the option of the blue grotto is available however, this depends on time and water conditions. the cost is 11 euro for the boat to take you to the entrance where you exchange boats and pay a further 8 euro to go in. is it worth it? having been in 1000 times, my answer is no. i would strongly advise you to take another option...a full 1 hour cruise around the island visiting the green, coral and white grottos. this also takes in the faraglione rocks and is a perfect 1 hour seeing capri at its best. the cruise around the island costs 11 euro.
if you want to take in sorrento also then book a single ticket from naples to capri on the jet. from capri to sorrento take another jet (20 mins crossing). tou could spend some time in sorrento. if you then choose to call it a day you can take the "circumvesuviana" train from sorrento to naples. the trains run every 25 mins and cost 3.20 euro. the journey time is 1hr and 10 mins. however, should you wish to include amalfi then after time in sorrento you can take the "sita" bus from outside the train station in sorrento (opposite piazza lauro). the sita busses operate every half hour and cost 2.00 euro. the journey will take you along the amalfi coast passing positano, praiano, fiordo di furore and takes just over 1 hour. after time in amalfi you could then take the "metro del mare" service from amalfi to naples.
it all depends on how much time you have and how long you want to spend in these palces. you can get the metro del mare timetable at
http://www.metrodelmare.it . should you like me to e-mail you the timetables for all services please do not hesitate to ask. the information is all upto date as i live in sorrento.
have fun