A few thoughts, some of which have already been mentioned above ...
"Theme park view" is a separate room category at Polynesian. It is available in Tahiti, Tuvalu and Aotearoa.
The definition of "theme park view" is an unobstructed view of Cinderella Castle. Not a panoramic view of all of MK, just an unobstructed view of the Castle.
"Lagoon view" is just that, a view of the lagoon. In many cases, one room may be TPV and the room right next door a LV, the only difference being a palm tree blocking the view of the Castle from that LV room.
As mentioned above, Hawaii is exclusively a club level building. In other words, you can't "request" Hawaii, as that would be requesting a free upgrade. Now, in Hawaii, there is no such thing as a TPV room category ... all of the rooms that face the lagoon are LV category. Yes, sure, many of them also have great unobstructed views of the Castle, but Disney simply doesn't sell any TPV-category rooms within the club level category.
You really want to avoid requesting a specific room number. The odds of that exact room being available are pretty low, and the rooms assignor will have no way of knowing why you wanted that number (lucky number? stayed there before? psychic advised you to pick it?), and if it's not available you'd just get any old room.
MY ADVICE? Definitely Tahiti, 3rd floor. WHY? You get a wonderful panoramic view of not only MK but the entire lake area ... starting from the left ... Wedding Chapel >>> Grand Floridian >>> tippy-top of Splash Mountain >>> tippy-top of Big Thunder Mountain Railroad >>> Cinderella Castle >>> Main Street train station >>> tippy-top of Astro Orbiter >>> Space Mountain >>> Contemporary Resort >>> tippy-top of Wilderness Lodge >>> monorail track >>> TTC ferry dock. You have a lot of grass and then a nice stretch of mostly unused beach right in front of you, meaning you're in a quiet neighborhood. I also really wanted to be relatively close to the TTC, which made going to Epcot so very convenient. It also made the bus trips back from Disney's Hollywood Studios and Animal Kingdom very convenient, because we could get on which ever bus came first, the one going back to Poly or the one going back to the TTC (and at each park those 2 stops are right next to each other). To me, the only downsides of Tahito were that we were kinda far from the Great Ceremonial House, and we saw the Electrical Water Pageant at an angle rather than head-on.
TUVALU was not my choice for three reasons: 1) I really wanted a balcony, and there are no balconies on the 2nd floor (meaning there's a lower percentage of them in this building than in Tahiti, which lowers my chances of getting a balcony); 2) It's nowhere near the TTC; 3) it is basically right ON the lagoon, there's no beach in front of it. Some people may ADORE that feature, but I wanted some shoreline in front of my room because I enjoy that better (in real life, I actually live in a beach resort town).
AOTEAROA ... uggghhhh ... don't get me started on that one as a location for a TPV room. Yes, to me it has one of the same drawbacks as Tuvalu, the thing about balconies. But there are many, MANY other reasons to be dissatisfied with a TPV room in Aotearoa. I listed them by number below:
1) Look at a map of Polynesian. Aotearoa is situated fairly far back from the lagoon. Yes, you can see the lagoon, but there is A LOT of real estate in-between you and the lagoon.
2) Yes, you can see Cinderella Castle from each TPV room in Aotearoa (by definition). HOWEVER, Cinderella Castle is pretty much THE ONLY part of MK you'll see from there. If you look straight ahead from Aotearoa, you have a wonderful view of Grand Floridian. You have to look a little to the right (about "1 o'clock," if you know what I mean) to see the Castle, but thanks to the fact that the Fiji longhouse juts out into the lagoon, your view of all of the rest of MK is blocked. In other words, you have a sort-of tunnel vision view of Cinderella Castle.
3) The side of Aotearoa that faces the lagoon also has the walkway that most people take to walk to and from Luau Cove for the Spirit of Aloha Polynesian Luau. That is A LOT of foot traffic going by your room four times a night (2 shows a night, each coming and going). A lot of noise and hustle-and-bustle, and not a lot of privacy at those moments ... no thank you.
For my stay last February, I booked a TPV room and requested 3rd floor Tahiti. I checked-in at 9:45 a.m. and was told that my room was ready. It was 2nd floor Aotearoa. YIKES! It was everything I didn't want ... it was the building I really disliked AND it meant I didn't have a balcony. I nicely asked the CM at the front desk if I could get my request granted. She got on the phone (I imagine calling Housekeeping) and after a minute or two told me I could indeed get a room in Tahiti 3rd floor but it wouldn't be available until maybe after 3 p.m. I said "THANKS!" We left our cazrry-ons to be stored by Bell Services (our checked luggage was being handled by DIsney's Magical Express) and we went to Magic Kingdom to start our vacation. As it turned out, our room wasn't ready until about 5:30 p.m. Yes, that was a royal pain in the neck, but it was well worth it to have that room for the next 7 days and nights.
We really cherished having a balcony. We watched Wishes from our balcony at least twice, as well as the EWP a few times, too. And since I'm an early riser and my wife and kids are sleepy heads, I could sit out on the balcony and read and listen to my iPod around dawn and not disturb the others. It was SO COOL watching and HEARING the Magic Kingdom wake up in the morning.