Hi!!!
I am so excited to hear that your family is planning a Disney cruise in the Mediterranean. I can tell you that it was the most memorable vacation that we've ever experienced. Touring the foreign ports and then being able to return to the comfort of the Disney Magic was a great way to travel!
We booked our cruise and airfare through the Disney Cruise Line.
I booked our hotel in Barcelona on our own. We stayed at the Hotel Novotel Barcelona City. It worked out really well. We stayed there one night prior to our cruise and two nights afterwards. It was nice having some time to acclimate to the time change before the cruise and fun to tour Barcelona afterwards.
This hotel had recently opened and was in excellent condition. While the location was not in the city center, it is in the "new area" and conveniently located to the Glories Metro stop as well as the Glories indoor/outdoor shopping mall. At the mall, you'll find a Carrefour store complete with a grocery area, McDonald's, Dunkin Coffee (and yes, they have donuts too), Subway, several local sandwich shops, toy store and more.
I booked this hotel on-line and got a great deal for a room that would accommodate the three of us. Many European rooms will only accommodate double occupancy. Our room had a bed and a sofa sleeper. We were provided with hand soap bars, shampoo/conditioner and shower gel.
If you google "hola disney journeys", you'll find information that I wrote on arriving to Barcelona.
Arrive early! Know how to at least say "hello" and "thank you" in the language of each country that you are visiting. Use ATMs for Euros. It's a port intensive cruise so pick your top sights to see and allow some time to relax on the ship.
If I can help any further, stop back with more questions and allow me to relive our magical voyage. Best wishes for a magical cruise in the Med!