Like many things, pool chair location preferences will vary from person to person.
First, let me say that Aulani is well laid out and fairly compact. Its takes less than 5 minutes to walk from one pool area to another, or from the beach to the pool, or to one of the eating places, bars, or drinks stations. If you had little kids you wanted to keep an eye on while they played in the water, then you might prefer/need one area over the over. But for adults, every area will give you about the same ease of access as any other.
If you something that is a bit more quiet, then getting chairs near the Wailana Adult Pool should be tops on your list. Since the Wailana Pool area is reserved for guests 18 and older, this area doesn't fill up as fast as the other pool areas that cater to families with kids. The sun doesn't hit this area until late morning, then you have sun until the afternoon. The Wailana adult pool is right next to the Ulu Cafe and the Wailana Pool Bar.
The Ka Maka Landing was added in October 2013. This is a good place to be to have immediate access to the Ka Maka Grotto Infinity Pool and Hot Tub, as well as the Keiki Cove water play area for kids. You can see a bit of the ocean and lagoon, especially when you are in the Infinity Pool. This area fills up fairly quickly.
The Infinity Pool also offers some great sunset views, too:
Waikolohe Valley is the name of the area that has Aulani's main pool, the lazy river, the Menehune Bridge Water Play Area, and Rainbow Reef, the enclosed snorkeling area. This area fills up faster than the other areas because lots of families want chairs near these features. Of course, the chairs that offer shade because of umbrellas or natural landscaping are grabbed first.
This photo was taken around 7:00 AM before the main pool opened (see the rope in the lower right). You can see some guests were already grabbing chairs.
Aulani is a beautiful resort, and when you are sitting by the main pool you can really enjoy its beauty. Here is a photo with the Ewa Building in the background:
And here is one with the Waianae Building in the background:
There are a few secluded spots scattered around that can be quite appealing. We found a few chairs next to a hot tub that was off one of the paths that meanders about the Waikolohe Valley. Here are a couple photos of my wife and the view we had from those chairs:
You can see the hot tub with the lazy river and the Menehune Bridge in the background:
The lagoon has lots of pool chairs that are free to Aulani guests, as well as some clamshells you can rent. The chairs will umbrellas are grabbed first.
There are chairs in front of the Ama Ama Restaurant which offer great views of the lagoon and ocean:
I think you just need to go to Aulani and pick the spot that best for you.