One week goes quickly. Best wishes and enjoy your honeymoon. Consider what to do once you finalize your plans. I have been to this area many times in late Sept. and up to mid Oct. weather is variable, this year it was cold and rained the whole time I was in Naples and Rome!
Do not book any boat trips until you get there, weather is a huge factor and seas are rough and small craft don't always go out. Others have mentioned May etc, this is totally different as Oct is off season for Capri. Stay one or two nights in Capri or Anacapri if it fits your costs. That time of year is lovely, but may be cold and windy for another boat trip...remember the ferry ride there is a boat trip! :) So you would take an hour ferry from Naples to Capri, then take a 3-4 hr boat ride around the island?? Then it would almost be time to go back to Naples, day trippers depart by 5p.m. or so. Since it is not a time for swimming, if anything I would do the regular boat tour 1 hr around the island, if you must, and not opt for private or shared with another couple trip, those are great in warmer weather when you want to park in a cove and going swimming or eat lunch. I think that a day trip should involve seeing the sites on the island itself...from up high. It is a very different island at night, so try to stay there. You can take a ferry from Capri to Positano and work your way back to Naples via bus and train....direct ferry from Positano to Naples ends in Sept. So Naples, Capri, Positano, Naples fly home. Or alternate trip, depending on weather, Naples 1 night , 2 nights Capri, back to Naples and directly to Rome for 2 nights, back to Naples 1 night fly home. There is nothing to do on the Amalfi coast when it is raining...but Rome can fill a rainy day and is only 1.5 hours by train from Naples, always take the fast train, slow regional takes 3.5 hours!
