Not necessarily "what cruise line?" but rather "what cruise ship?".
As for party-intensive, cruises where singles are looking to hook-up, Carnival and Royal Caribbean Spring to mind. Lots of single 20-somethings on most sailings.
As a general rule, the larger ships of most lines are a good bet, with emphasis on the big Voyager-Class ships of RCI, Grand-Class on Princess, and Destiny/Conquest class on Carnival. Avoid smaller ships and sailings longer than 7 days, as they (usually) attract an older clientele. Lines like HAL tend to seek the more mature cruiser.
I am not familiar with the ships scheduled to depart NYC and New Jersey this summer, but they do tend to be newer, larger ships. There are lots of families cruising at this time, too.
Just 1 month to go until the "Cruise Cynic Mystery Cruise" ... January 2008
there are so many variables and personal choices to consider. I would suggest that they get brochures from Carnival, RCCL and Princess, study the brochures, its not just the ship to consider, ports of call are a huge factor. They should look into the bigger, newer ships, summertime is peak travel time for families on all major cruise lines. Each line/ship is different and has a different appeal.
We were on the Dawn from NY this past November, really good mix of all ages and plenty for them to do. My 19 year old was never in the cabin, I had to go find her several times. Ship departs right from Manhattan around 4PM and it sails past the Statue of Liberty and under the Verranzano Bridge, GREAT VIEWS of the city with the sun setting on it! Take a look, it was a great time.