It sounds like a movie plot: A band of down-but-not-out survivors come together during a crisis. In a world where Puerto Rico staggers under $70 billion in debt, Americans are emerging from the icy grip of a record-setting winter, and cruise lines like Royal Caribbean Cruises (RCL -1.31%) have hit choppy waters, can they find sunny sailing?

Royal Caribbean's megaship Quantum of the Seas debuts in late 2014. Photo: Royal Caribbean.

That's what investors, travel agents, and Puerto Rico's business community want to know. Royal Caribbean reported this month that first-quarter net yields dropped and net non-fuel cruise costs rose slightly. Competitor and industry leader Carnival Corporation (CCL -0.13%) reported similar yield drops and cost increases for its first quarter. A March oil spill in the Houston Ship Channel interrupted several cruises, contributing to the poor numbers.

More travel, more Caribbean cruise deals
Despite the lackluster first-quarter figures, Royal Caribbean's outlook for 2014 is positive, with full-year net yields expected to rise 2% to 3% and adjusted earnings per share in the neighborhood of $3.35, with new ships on the way.

Rising spending among U.S. travelers is helping boost leisure trips overall, and with airfares and hotel rates going up, too, cruising is looking more appealing. To put some wind in their sails, Royal Caribbean and competitor Norwegian Cruise Line (NCLH -1.30%) have just launched buy-one get-one deals on selected cruises.

All of this is good news for sun-seeking families. According to TripAdvisor's TripBarometer global report released earlier this month, beach vacations are among the top five choices for families, who are generally the most price-sensitive travelers.

The Caribbean cruise deals could be good for Puerto Rico's economy, too. The territory's popularity as a destination has been growing, with more than 940,000 cruise visitors from July to March -- a year-to-year increase of nearly 125,000 people, according to the local port authority.

A report from the Florida-Caribbean Cruise Association trade group says cruise passengers and crew spent $186 million in Puerto Rico during the 2011-2012 season and supported nearly 5,000 local jobs. More cruise ship passengers are expected in San Juan over the next two years.

More Puerto Rico port calls on the horizon
Royal Caribbean's new megaship (Quantum of the Seas) will dock in San Juan this December. It will bring up to 4,180 passengers into port, assuming passengers leave on-board indoor skydiving and surfing long enough to touch land.

A pier expansion is under way to accommodate that ship and its sister vessel, Anthem of the Seas. Anthem will start cruises to San Juan and other Caribbean locales in 2015 from its home port in New Jersey -- an ideal location for Northeast corridor residents looking for a break from snow days.

2015 is also when Carnival will start new one-way sailings between Galveston and San Juan that make a 21-day loop through the Caribbean with no repeated stops. Walt Disney (NYSE: DIS) subsidiary Disney Cruise Line, meanwhile, is home-porting a ship in San Juan for the first time this fall as a base for four late-2014 cruises to southern Caribbean ports including Grenada.

A happy ending for Puerto Rico's economic woes?
All of this extra cruise business should be a boon to Puerto Rico's struggling economy -- and a confidence booster for U.S. investors, who've been reluctant to put money into the industry. If enough travelers take advantage of the cruise lines' competitive pricing and new itineraries, Puerto Rico (and the cruise companies that dock there) may emerge as a crack team of leisure-travel heroes.