Here's what we did:
Kotor: We booked a tour through Viator ("Lady of the Rocks and Blue Cave - Kotor Boat Tour "). It was great. You end up on a small boat with 10-12 people, so a lot probably depends on your captain, but I really liked ours. It was just a very beautiful boat ride through the bay, the soviet sub tunnels were interesting, and the blue caves were very cool to see. There were plenty of people getting off the ship and buying a ticket for the exact same thing we did, so you probably don't need to pre-book unless you want to.
Dubrovnik: My favorite day. We didn't pre-book anything. We got off the ship first thing and took a taxi to Old Town (it was 18 euro for the taxi...the ship also offers a shuttle for $20/each). We paid to walk around the walls (35 euros) and did that for a couple hours. We then took the cable car up for some great views. There was a small museum up there as well (5 euros?) with a few artifacts, maps, etc from the Siege of Dubrovink in the early 90s that I found interesting. I wish I had read up on it before we went because some of the english translation within the museum was a little iffy. I was very young in 1991 so don't have a lot of memories of it happening. We then went back down and found a great restaurant for lunch (don't remember the name, sorry) in one of the alleys. I would definitely recommend doing the walls and walking around the Old town as early as you can - one because it was hot and two because by the time we finished lunch, it was absolutely packed. Plenty of taxis to take you back to the ship as well.
Mykonos: We did the NCL excursion to Delos which I found really interesting. Our guide was pretty good which helped. You can also book this yourself. Not sure how true this is, but our guide said since we booked through NCL we got there earlier than most of the other tours. It was pretty empty when we got there, and it was starting to get busy when we left. After the tour, we walked around Mykonos for a few hours and grabbed another good lunch.
Corfu: We did the NCL beach break here. We were looking for a "chill" day since there were no sea days. This was just a bus to a local beach club. The beach club assigned all the cruise passengers beach chairs in the back (some even on the grass behind the beach where you couldn't even see the water). They left the better chairs for customers walking up and paying. We ended up going to the beach club next door and paying 20 euros for a better chair.
Zakynthos: This one I wish had just been our chill day, and that we had done something different in Corfu. We ran into some of the same issues you are facing trying to plan. We wanted to do one of the boat tours, but with the schedule getting adjusted it was hard to find a tour that met our timeline and wasn't a private charter (it was just 2 of us, so we didn't want to pay for a boat for just ourselves). We ended up doing the Panoramic Zakynthos through NCL, and it was not great. Our guide wasn't very good, and it was a lot of bus time to see some not that exciting things. Not sure if it was just a one time hiccup, but our tender line getting back on the ship was also very long (+1 hour).
Overall, Dubrovnik, Kotor, and Mykonos were my 3 favorite stops, in that order. If I had it to do it over again, I would've done something different in Corfu and made Zakynthos either a sea day or a light day to just stroll through the town on our own.
Hope that helps!
