How to reach ?
There are many ways by which you can reach Capri. Either take a flight to Naples (nearest airport) and then a cruise from Molo Beverello (takes about an hour to reach Capri)or there are also day trips directly from Rome with hotel pick up services (They take you by bus till Naples and then cruise to Capri).
Where to stay?
You could stay near the beach in Capri , but that’s going to cost a lot, considering the fact that this island is the hotspot of the rich and famous. So just in case you are a Budget Traveler or you want to save some bucks, you should check out Anacapri which is located at a higher elevation on the island than Capri. I wouldn't say the stay in Anacapri is cheap, but it is pretty less when compared to Capri.
And If you have booked a stay at Anacapri, then be prepared for a long queue at the Bus/Taxi stop, as the only way up is by public transport. The bus frequency is every 30 mins and due to the narrow lanes the bus size is quite small. The Bus ride is adventurous as it takes you through the narrow lanes with hairpin bends & twists around the curves dangerously close to the edge. And it’s not a good idea to walk with your luggage as it’s a climb uphill.
We booked our AirBnb at https://www.airbnb.com/rooms/5937686?location=anacapri&check_in=2017-08-17&check_out=2017-08-18&s=19xDl_Uw