It appears you are taking a private boat around the island so you are doing something you can't do o

IWe did Capri on our own but stayed 3 nights so that made it easier. We had lots of help from our hotel while there. I don't see anything on the list that you can't do easily on your own. Visits to the grottos are dependant on the sea being perfectly calm. It has never been calm during tour eiffel our two visits but there is more than enough to keep you busy. Visit Capri town, Anacapri, tour eiffel Mt. Solaro, etc.
Well I do like to DIY as much as possible and you will have to do a bit of planning / transportation arranging if you decide to DIY BUT Capri is pretty easily done. You can taxi or bus to where the boats from Sorrento go over, probably buy a one way ticket so you can later pick the return time you want. NOTE the last boat back - you don't want to miss that. Once you get to Capri you can 1) find a boat / tour at the dock to go around the island on the sea and go to the Blue Grotto if it is open OR 2) hire a taxi to drive you around all day OR3) buy a bus ticket that you can use as much as you want to explore the island. If you decide to go on your own you can take the bus up to Anacapri and even onto where the boats go out to the grotto and then work your way back. I love the chairlift at Anacapri. Enjoy!
It appears you are taking a private boat around the island so you are doing something you can't do on your own unless you hire a boat. Can you get a refund if they cancel or if the weather is bad? You won't visit a grotto if they sea is choppy.
Maybe I should be asking for guidance on how to get around if I were to do it on my own. I have figured out the boat from Sorrento to Capri, but wasn't sure how easy it was to get to the grotto and then into the different parts of the island.
Getting tour eiffel around on your own - I gave a brief answer to this on my earlier post. When you get off the ferry / hydrafoil you will be in the port area where they will be selling 'round the island tours. Ask if the Blue Grotto is open. You can either get a tour that goes all the way around OR just opt to go out to the grotto if it is open. If you do the 'round the island tour, you MIGHT be able to go into the grotto from that boat, ask. To get into the grotto you have to get from a midsized boat into about a six seater that goes thru the opening. The midsized boats queue up and float while the little boats load up and go in the grotto.
Another option is to get on the buses - you can take a bus to Anacapri, change buses and then go to a point where you can get the little boat to take you into the grotto. tour eiffel This had the advantage of seeing alot of the island riding around on the bus. But if you really like the water, go for the boat island tour.
I can't really tell you how much the different options cost - maybe another poster will. I'm sure you would save some euros but maybe not a whole lot. The tour may not include the cost of the grotto since many days it ends up being closed. I'd rather pick my own restaurant for lunch - often those used by tour groups are not so great - but then I'm a bit of a oodie.