Planning a trip to Greece

Greece is quite easy to do on a DIY basis. You have not told us your dates so I just did a random booking for ferries in mid June. Athens (Piraeus port) to Mykonos has 5 daily departures. The shortest is 2.5 hours on Seajets Championjet. The other 4 are 5,8,5 and 5 respectively.
You could also consider traveling from the second port at Rafina which is fairly close to the airport. Seajets is the fastest time at 2 hours and 10 minutes. From Mykonos to Santorini there are 8 departures the quickest is Seajets Championjet at one hour and 50 minutes.

It would be interesting to understands what benefits of your independent tour is providing to you if they can't tell you the timing of ferry routes. As I said it is very easy to plan your own Greek vacation and probably at a far lower cost than an organized tour.
I have seen cases where people have come onto a Greek forum checking the value of an organized tour Particularly the hotels and discovered they were paying a third more for the tour than booking directly.

For example I got the ferry names routes and time in about 3 minutes on https://www.ferries.gr/greek-islands-ferry/.

Try it yourself on your exact dates.

Also once you have your hotel name and dates run the hotels through Booking dot com. You will get price availability location on a map and most important reviews. You should be looking at a review of 8 or better. Anything lower probably has some issues.

Just because I am feeling mischievous this morning I have to wonder at the island choices on this tour. I understand Mykonos and Santorini are the most heavily promoted Greek islands and in fact I fully believe Santorini is a must see Island for that caldera view. That view is very expensive but if your budget can stand it for three days that is about optimal timing for Santorini. After that the cost and the Cruise ship crowds start wear us out.

Santorini http://www.flickr.com/photos/stanbr54/sets/72157632154800782/

Mykonos on the other hand has chosen to Market itself as a high end tourist destination with lots of expensive shopping. Hotels and dining are priced the same as Santorini however nearby non cruise ship Islands of Naxos and Paros offer equally good beaches, mountain villages, beautiful old towns and Naxos has the Venetian Kastro topping the main town. All of this on similar ferry routes and at less than half the cost of Mykonos.

There I said it.
Naxos Town http://www.flickr.com/photos/stanbr54/sets/72157632094558042/
Trip around Naxos http://www.flickr.com/photos/stanbr54/sets/72157634605629689/
Naxos sunsets https://www.flickr.com/photos/stanbr54/albums/72157700728046481

One other thing to consider sequence of Islands. Experienced travelers on this forum generally recommend you leave Athens until the end of your trip particularly if you have a transatlantic flight. Getting over jet lag on an island is way better than doing it in Athens. We always fly to our first island with a connecting flight the the furthest island. In your case Santorini. Then ferry to Mykonos and Athens. It is wise to be in Athens for a minimum of a day before your return flight. Athens really requires three days to do it adequately. The reason we like to fly to our first island is cost of flights is often about the same or a little more than the fast ferries. For instance you have not told us how you plan to get back to Athens after Santorini. That is a 4 to 5 hour fast ferry trip with commuting to and from the ports you can add on another two hours onto that trip. Flying can gain you almost a half day of vacation over the long ferry hops.

I realize I have done some assumptions for this response. It might have helped if you told us your dates, budget, interests and where you are coming from.

Greece is a great place to visit, have fun.

Both Santorini and Mykonos are small islands that are simple to navigate on your own. Unless you absolutely need a tour guide you can easily explore them on your own and save money in the process. Ferries and planes will take you from Athens to either island in 30 minutes and a highspeed ferry will take you between them in less than 2 hours. Take the time before you decide to see what these islands have to offer. Buy a good guide book for research. And Trip Advisor has forums for both and you can look at "Things to do" at the top of each island's forum page. Same goes for Athens. But save Athens for the end so you aren't backtracking and so you don't have to scramble back to the mainland at the last minute for your flight home. Also, it's rare, but there are sometimes ferry and flight cancellations at the last minute that can cause you to miss your homeward flight (another reason to not try to fly home the same day as your return to Athens).

Spaniel I am sure you are going to have pefect time in Greece.
Taking the ferry from Rafina would be much better as it is less hours but you have to keep in mind that they are small ships if you have problem of motion sickness. It is also far away from Athens. I would suggest you to go by plane. There are many flights for Santorini and mykonos. Check Ryan Air.
For both islands you do not need a tour. They are both very small islands. Becareful in mykonos as even if you rent a car there is too much traffic and problem with parking
In santorini rent a car or bike. I would suggest you to swim in Kamari beach... Imba restaurant the best and Theros eat at Psaraki
In mykonos visit Agia Anna beach and eat at Vracho and at Panormo beach.
For athens I would suggest you the Red bus. Also it is better to take a guide for visiting museums and Acropolis, palia agora. A nice restaurant is Mani Mani and ellinikon. Visit Agia eirini for drink. What is unique to do is to watch a theatrical performance of Ancient Drama. These performances arenew in Athens so you may not find them in touristic guides. Fimonoi is one...
Have perfect time and If you need sth fell free to ask