Welcome aboard! We did this cruise on Norwegian Jade in April 2010. Monte Carlo is definitely walkable, yet be sure to wear comfortable shoes as the hills can be steep. As for Palma de Majorca, NCL runs a bus ($10 per person for the entire day, payable on the ship) from the pier into town, across a busy street from the Almudaina Palace and Catedral La Seu. We walked around town, especially enjoying the a stroll down the pretty Passeig des Born. We were too early for beach season, yet there is a public bus system that I have heard goes there. Check our Ports of Call section, as Penny suggested, as there are a couple of topics on Majorca/Mallorca/Palma beaches.
Are you embarking in Barcelona (as we did) or in Rome (Civitavecchia)?