I'm no expert cruiser, by any means. But, our family knows what we like and what we don't.
Alaska...not going to say much about that aspect. We loved Alaska, and would recommend it to anyone.
The Jewel- generally positive, with a few areas that could use improvement. This was our first "freestyle" cruise, so I'll touch on what I liked and didn't.
Rooms: 5 in our party, so we had a balcony and an inside room just across the hallway. Booked via phonecall to Norwegian, they were SUPER helpful. Inside room was pretty small, but efficiently organized for our 3 children (18 to 23 in age). Room for my wife and I was a balcony. For 2 people, a balcony is very nice, and our whole family fit in it well enough when we all wanted to be together (cruising up Tracy Arm for glacier viewing, for example.). Many people might like that the balcony room had a king-sized bed. We would rather have had a smaller bed and a little more floor-space. Its a tradeoff I suppose, would you rather have a big bed with less living space, or a smaller bed with more living and storage...we'd have preferred a bit more living room.Bathroom was very nicely organized, although if you had long legs, you might feel cramped by the toilet orientation. Storage in both rooms was adequate and pretty intelligently designed. Closet had plenty of hangers, which was very much appreciated.
Public areas: comfortable and spacious. I was concerned that with so many "for fee" dining options, there wouldn't be much space for public areas. But, even with a full ship, we never felt cramped, and all areas were quite nice. And, after Carnival's sometimes "over the top" gaudy embellishments, Norwegian's lower key design was refreshing and pleasant.
Dining: Ok, I admit it, our family is cheap when it comes to food. We did not pay anything extra for the special dining venues, preferring to use the "free" dining rooms and buffet. We had lunch once in the Blue Lagoon, which is a fine choice for a quick sandwich or something like that. Food there was served quickly and although simple, was quite tasty. We ate once at Azura, the "casual" dining room. It was the first day of the cruise, and we were not impressed by the service, although the food was fine. Azura seems a little smaller than the more formal Tsar dining room, and seemed more cramped and noisy. Food was Ok, but we never went back. Most evening meals were in the Tsar dining room. Very elegant setting, but with freestyle dining, you are fine showing up with jeans and a polo shirt. Service was very uneven. Early in the cruise, they were slow, later in the cruise service was much more efficient. I will complain that tables were often not set properly, (missing some silverware or glasses, etc), and the tables had fancy salt and pepper grinders, which often did not work, which was annoying. However, except for a couple of wait-staff lapses early in the cruise, service was generally good, and sometimes excellent. Food was variable, generally quite good, sometimes excellent. Try the bread-and-butter pudding, a bread-pudding that's just exceptional.
Buffet: plenty of variety for all meals, and it was all pretty tasty, for buffet food. It was obvious that many people never bothered with the dining rooms and ate most of their meals at the buffet. And, that's fine, but that makes the buffet very busy and noisy, and, if you only eat at the buffet, you are really missing out on the much better food and service you can find elsewhere on the ship. Nothing against Norwegian's Buffet, the food is just fine, but, it's still mass-produced buffet food. Nuff said.
Beverages: My wife got the soda package (6 bucks a day, free soft drinks), because she needs her Pepsi quota every day. Norwegian was excellent in this aspect, my wife just had to flash her card, and the drink was coming, nothing to sign, no questions about who the drink was for (Carnival should adopt a similar policy on their soft-drink package) Beer and mixed drinks? Good, prompt service at the bars and from the waiters circulating around the bars and pool area. With 4 in our party 21 or over, we usually got the "bucket of beer" special (buy 5 beers, 1 is free, includes domestic and imports, and you can mix up the beer as much as possible). Bar staff at the pool was especially attentive, by the end of the tour they would spot us, call us by name, and ask if we wanted a bucket of beer (and we usually did).
Pools/Hot tubs: I wasn't sure if we'd use the pools much on an Alaska cruise, but the weather was great, so we did. The Jewel has two pools, one of kids, one (supposedly) for adults. On busy at sea days, no one policed the "adults only" pool, so it usually had as many kids as adults in it, which was annoying...Carnival is much better in this aspect, with their adults-only Serenity decks. Another quirk about the pools was the depth. Both pools ranged between 5 and 6 feet deep. No shallower areas in either pool. If you've got kids, bring some type of floatation for them. Seemed weird to me that only six footers would feel comfortable just standing in the pools, and that shorter kids had to pretty much hang onto the sides of the pools all the time. I'm 5'8", and I mostly had to tread water all the time, which is not very relaxing. There were 5 hot tubs, the two beside the adult pool were nice and warm, the other 3 were comfortable, but not warm enough for "serious" hot-tubbers (but probably fine and safer for younger children).
Entertainment: We took advantage of a wide variety of entertainment, and it was all anywhere from Ok to excellent. Trivia, game-shows, beer-tastings, music at lounges, comedy/magic/hypnosis shows, and big variety shows. All pretty standard cruise-fare, and all pretty good.
Freestyle: Norwegian pushes the "do what you want when you want" which sounds good, but really most means "eat what you want when you want" more than anything. With our family, that worked great. If it was just my wife and I, I think we would have missed the assigned seating and dining times of other cruises, with the making of new friends and the lavish attention of the same wait-staff every night. But, that's a personal thing, I suppose.
Cleanliness: Excellent! Norwegian obviously is serious about keeping things clean. They even have people as you enter the buffet with spray bottles of alcohol, spraying your hands while singing "washy-washy, happy-happy"...its a good idea!
Overall-Norwegian has a nice recipe for success, and they succeeded. It might not have been perfect, but it was pretty darn good! We had a great time, and were well cared for. Will we cruise Norwegian again? If the itinerary and price is right, sure.