Yes you can do DIY at Crete,Rhodes and Mykonos but I wouldn't advise it at Santorini. The gem there is Oia and not Thira and to take that in within the time you really need an organised trip.
Very easy to DIY in each port - advise you ports and we will help - otherwise research via ports of call on web site called cruise critic.
We are also going in July on this ship and we calling at Split, Heraklion, Kusadasi, Santorini and Corfu and any information on recommended trips and also DIY would be appreciated. Hope Aldrich can help.
Santorini: We took the first tender off the ship, rode the funicular up to Thera, and caught a local bus to Oia. VERY EASY to do on our own, and very cheap, and because we made sure to go to Oia early, the bus cost €1.5 and leaves 8.30, 10.00, 11.15 - and on the return leaves 12.50 and 14.30 - wouldn't advise leaving it any later but if you do a cab is €20.
Split: We called at Split last year, and found it a very attractive port. Ship docks very close to town there was a market, quite interesting shops. The town centre is built on the remains of the Diocletian palace and is a mixture of ruins, deep cellars with shops, narrow streets. The seafront has lots of bars and cafes. Unless you really fancy one of the ship's tours, I would just spend a couple of hours exploring on your own. The currency is Kuna, and whilst in town they accept Euro outside they prefer their own currency.
Corfu: A taxi ride to Old Town is about 15 Euros. It's a 30-minute walk from the port.
Corfu Town has one of my favorite restaurants in the world...We ate there on BOTH visits...It's called, believe it or not, "Pizza Pete's"...It's not the food that makes it special, but the location...As you walk into town you can see a promontary as you start going up the hill - it is right there. The tables are on a covered patio across the road on the cliffs...Get a table right along the rail and you have an incredible view looking straight down at the rocks and water...The waiters take the leftover bread from the tables and throw it down into the sea and the fishes put on an unbelievable show fighting for the scraps of bread...You can see the entire strait across from you clear to Albania across the water...
Pizza Pete (Arseniou 21. Tel: 06610 223301).
Haven't cruised to the others so can't advise on those! Suggest you try ports of call on cruise critic for some advise.