You knew I would jump at the topic. But since we have never been to Dubrovnik (2 cruises to that port were cancelled) I can be of no help. As to Kusadasi, you are in for a real treat since Ephesus is perhaps the most amazing ruins on earth. If you do not want to go on the ships' tour, than you should arrange for a decent private tour on-line. Its also possible to just pick up a taxi and guide at the pier, but many of those guides are not the best. This is one of the few places that I strongly recommend you do not do on your own for the first visit. These ruins beg for a decent guide to bring it to life. Ephesus will only take half your day. For the other half, right across the street from the pier you are in town and they have an outdoor market (bazaar)that starts on the other side of the street. Its lots of fun, but be prepared for strong bargaining.
Santorini - Easy to do on your own. You just take the tender in to the marina, than you can get up to the city in the cable car or donkeys. The city is a place that you walk, and its wonderful and one of the most picturesque places in the world. If you get bored with the town (its called Thira or Fira) you can grab a local bus (about $2) to the other well-known town of Oia (much more laid back and residential). There are also beaches and wineries on this island and they are best accessed by simply renting a car. But for a first visit the two towns usually make most visitors smile and fall in love with the island.
Corfu - A pretty large island that is very tourist-friendly. The town (Corfu town) is walkable and has many shops, cafes and decent restaurants. If you want to explore the island its a good place to rent a car (pre-arrange on-line) but your short port day might make this a bad option. This island is the main island if the Ionian Islands, and its a major yachting haven during the summer months with many Brits and other Europeans making it their base. English is widely spoken and its a place where most feel very comfortable on their own.