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Try Princess cruises. My parents just got back from a trip on a Princess ship and really enjoyed it. Many food options and your didn't have to get locked into a set dinner place/time. Entertainment was plentiful, and for all tastes.
They docked very early on the return in and were even fed breakfast before leaving the ship.

@allakarasik: Thanks so much for the information. I know a number of people whose parents love to cruise. Could it be a generational thing?

I wonder if this question is geared too far toward the "travel spectrum" and not within the "Serious Eats topic" spectrum. Though, food and travel usually go together for me.

Perhaps people who really love good food opt out of this kind of thing because of a shared perception that cruises produce food quanity instead of food quality?

Oh wait! It wasn't Norwegian, it was Holland America!

@wookie: I agree, the food on Carnival is typically mediocre at best (in the regular dining rooms). However, the pay-extra restaurants cook their food a-la-minute and rival some of the nicer steakhouses available on land. It's the best of both worlds (except you have to pay a little extra).

@susquehanna: I know a lot of people in my demographic (25-34) who like to cruise as well. It's appealing because you only have to unpack once and you don't have to worry about anything once you get on board. It's also very flexible -- you can dress up for dinner or go casual in a different dining room. Just try to make sure that you find restaurants in the different stops that aren't infiltrated by the thousands of tourists you'll be traveling with!

Dominic
the zen kitchen

Your best bet is to go with a company that specializes in small ships.

Depending on your budgetary considerations, the best of these (at the luxury end of the spectrum) would be Crystal Cruises, Silversea or Regent Seven Seas. Although they are very expensive, if they are within your means, a little research will reveal that they actually can represent an excellent value, particularly since they tend to be longer cruises and come closest to being truly all-inclusive (other than airfare and special shore excursions). They also are very small, intimate ships with very few on-board restrictions (in terms of dining times, seating, etc.). They have a lot of foodie-friendly special cruises, too, with cooking classes, culinary demos, guest chefs, etc., which is how they came across my radar.

A little less expensive and also marketed as "alternative cruising" (e.g., anti-Carnival), are lines like Windstar and Oceana. Windstar tends to attract younger, more active cruisers, with lots of physical activities offered (scuba, surfing, etc.). If you'd enjoy an ultra-casual, sportier type experience, check out Barefoot Cruises, which rely on sailing vessels, and allow guests to participate in vessel operation if so inclined

Once you know which lines offer smaller ships within your budget and timeframe, be sure to do your homework as to things like hidden charges, add-ons, and -- extremely important -- ship culture. E.g., what is your age vs the age of the line's typical customer? Do the ships' activities match your interests? Some offer athletic activities, or cater to "young" travelers, while others will have shuffleboard as the most strenuous activity. Is it 100% casual or are there mandatory formal dress events? Etc., etc., etc.

Carnival cruises are party ships, other lines are a little more refined, I guess you'd say. We've been on a number of cruises, and the best tip I can give you is to talk to the crewmembers and ask them where to go eat onshore that isn't touristy. Or, depending on the port, just get off the ship and hail a cab as ask the driver to suggest a good place. What's the worst that can happen? You waste a few dollars and you go back and eat on the ship later.

I've been on Royal Caribbean and Celebrity cruises a few times. Celebrity had really good food which is to be expected since it's a step up from RC. The biggest difference we found re: the quality of food (and other things) is the length of the cruise. I'd aim for a longer cruise (i.e. 6 nights at least) since the shorter ones just really aren't as nice. Everything's a step down, including the food.

I'd also check out a site like CruiseCritic - I imagine a number of people on there can probably give feedback on the food options available on the different lines.