A good umbrella stroller is helpful, especially on larger ships. Harmony of the Seas is a big freakin ship, and if I knew we'd be out for a while without a seat in sight, we brought the stroller out from the room. An umbrella stroller is best because it's lightweight, fits through the narrow doorways, and folds up out of sight in the room. I've relied on a Chicco Liteway (or the Plus version) for most of my cruises. It's my everyday stroller too! We kept it by the door and just moved it out of the way as needed. By the end of the week, my one year old figured out how to push it against the door to grab the handle and looked like he was trying to escape!
I've also been recommending portable tubs since my very first baby cruise, back in December of 2013. They can be used as a tub within the shower for little ones who aren't accustomed to water falling on their heads. They can also double as a splash pool for use on ships that do not have a diaper friendly pool area. Now, most suites come with tubs and some regular rooms on lines like Carnival and Disney also have them too, but you'll need a savvy travel agent to help you locate which rooms those are and which ships have diaper friendly areas by the pool ;)