First trip to Greece - taking daughters - Girls trip!!

You will go through Passport Control and Customs in Munich. After you collect your bags in Athens just go through the "Nothing To Declare" door. No one will question you. Give yourselves a 2-hour window to catch your Naxos flight. Take the 2-hour Blue Star ferry to Santorini, leaving Naxos around 1pm so you'll be on the open deck of a conventional ferry when you first enter the Santorini caldera. It's a wonderful memory you'll never forget. The other boats are all enclosed catamarans and you'll only see it through salt-glazed windows.

Personally, I would use the time you have allocated to Hydra for either Naxos or Santorini.

You seem to have a good plan. I can only add my voice to the advice you have already received.

Hydra is a recommended island primarily for people who do not have sufficient time to visit one of the Island chains. Since you are planning Naxos and Santorini I would suggest you just add the Hydra time to one of these islands. Naxos would be my choice.
Naxos Town http://www.flickr.com/photos/stanbr54/sets/72157632094558042/
Trip around Naxos http://www.flickr.com/photos/stanbr54/sets/72157634605629689/

The other reason we are suggesting dropping Hydra is every island hop you do eats up at least a half day of your vacation. Time is precious on a vacation and adding another island means you are spending time in commuting rather than taking advantage of one of your chosen islands.

Using that same logic we always choose the ferry that gets us to our next island the fastest. In September Seajets world champion jet departs Naxos at 10:30 and arrives Santorini 11:40. So you will be on Santorini before the next ferry the blue Star departs Naxos.

World Champion Jet is new this season so I don't know it but the Seajet Championjets have open decks at the back and the sides so you can be on the deck for arrival in Santorini. Hopefully world champion provides that same opportunity.

Thanks everyone for the great advise. We are going to drop the Hydra island. If we wanted to do a day trip to another island near Naxos where would you go?

How many days do you have in Naxos now? It is a big and varied island so I wouldn’t be too quick to take a day trip. We were there for four nights and really wanted one more. There are lovely beaches but there are mountains in the interior. Naxos town itself has medieval sections which are fun to explore. We rented a car for a couple days which allowed us to see much of it. We were a family group of 7 and we split up for part of the time. That is how we all know what we missed! Pictures don’t lie.

I agree . . . spend your extra time on Naxos. It's the largest of the Cyclades Islands with plenty to do. I stayed for 9 days and could have stayed longer.

However, if you want to do a day trip then the Delos/Mykonos cruise would be good. Delos is one of the most spectacular and lesser visited archeological sites in Greece. The island is a treasure-trove of history and has a wonderful museum. Mykonos is over-the-top touristy but it was part of the cruise. I thought it was not the type of "Greek" island for me. The day trip will take most of the day so it's a judgement call for you if you decide on the extra time on Naxos.

We just came here ( Naxos ) from Paros ( which we LOVED ) - ferry was 11 euros and took 35 minutes .
Issue may be your dates as ferry schedule does slow down as seasons wane - at this point now we had a choice of three ferries , but by later in September you at have only one or two .

If you come to Naxos ( it’s my third time here ) you could do what we did this time - we stayed in Naxos town ( chora ) for two nights and now we are out on Aggia Anna which is amazing , beach is much nicer than ones in town - and it’s only 15 minutes away by bus from town !

Thanks everyone, We want to stay 2 nights in Santorini. I am looking for suggestions of hotels. I'm not a luxury hotel type so I would like an apartment or Airbnb. Any suggestions? We will take the ferry from Naxos to Santorini. How easy or difficult is it to get to the other side of the island? Should we just stay nearest the port? Suggestions for staying in Santorini? Ready GO!

There are just too many options for accommodations to mention without knowing your maximum combined nightly room budget (in EURO) You don't need to stay near the port. Stay in whichever village you want. Take the afternoon Blue Star car ferry to Naxos. It leaves Santorini daily around 3:30. There's a bus to the ferry port you can catch in Fira. It leaves Fira about an hour before that 3:30 departure.