DO IT YOURSELF

Generally, yes, you can do much yourself. It is easier someplace like Istanbul, study ahead, get an idea of a plan, and go. Where it might take a bit more effort is places where the Cruise Ship Dock is bout the only thing around and most of the excursions are inland. In that case, you may find Taxis or independent guides advertising their wares near the dock, sometimes you can book ahead as well. Public transport is also an option, just be aware of schedule, often it may not fit what the ship is doing. I would do some searching for each locale, see if sights are near or far, then look for local tour companies.

Good advice above, taxis are almost always available although they may drift off after a couple hours after the ships's own excursions leave. I think you get more from the port when you have a tour booked, but you can 'see' the sights and carry your own guidebook with a taxi. I haven't looked at Rick's new cruise guidebook. Might be worth a good look. Private tours are less costly than the ship's, but IMHO more interesting, plus less time waiting for everyone else to gather and board the bus at multiple stops. You could indicate your own interests if you book ahead. Allow plenty of time for the traffic in Istanbul when returning to the ship. You might visit cruisecritic.com for details on some ports, or copy your own ship's excursions.

Do register on cruisecritic.com and then go to the Roll Call section and find your cruise. Many cruisers put together small tours similar to those offered by the cruise line, but at a lower cost, and with a smaller group. They are often looking for others to join them. You will also get ideas on what to see, tours by local operators and local guides.