First I would like to state that we are from Malta which is the first port of call after Barcelona embarkation. Secondly because I'm from a hot Mediterranean country I strongly advise the use of sunscreen, light comfortable clothing, hats and a steady supply of drinking water for every excursion you plan to take.
Take a very small lightweight stroller as you will have to stash this under your bed due to the space constraints we had a balcony but space was a problem. The crib supplied by NCL was essentially a travel cot playpen. The mattress was harder than our playpen at home so our baby ended up between us in our bed and the crib was returned after 1 night.
We took a very small inflatable pool for our 10 month old daughter as per Cruise Critic reviewer advice. It was a good decision as the babies pool was too hot and a very silly lady decided to feed her daughter in there once, leaving the water full of bits of food. The bar staff will happily oblige to fill a small baby pool up. We usually took a couple of chairs opposite the Topsiders grill and snacked there with our baby pool by our feet.
Great views from our balcony, cabin on the small side.