Investigate a variety of "independent" components throughout the world. They offer city tours, food tastings, bicycle & walking tours as well as many private and customized possibilities.
Escorted tours always have some "at leisure" time in the major cities. Plan ahead: "know before you go" how you maximize that precious time. Check out pre & post cruise options in addition to shore excursions as well. Independent travelers will find it helpful making it easier to decide what destinations may suit you best and/or help deciding how much time to spend or even that you might eliminate it all together. Explore what Project Expeditions has to offer.