That's a good question about the two free nights. Using no points I'd probably choose the Hyatt, but only if the rooms had been recently renovated. See below. It's a tough call because of the packing up and moving to another property after two days versus five days unhindered.

The Hyatt is directly across from Waikiki beach, but you may not end up with a beach view room though. They are going to save those rooms for the revenue guests and diamond passport members. I would call and/or send an email to the Director of Rooms and the General Manager and ask them when they last performed a soft renovation in the rooms. If it's more than 4 years the rooms are going to be tired. This goes for most any property.

I stayed at the Hyatt Place in August of last year after they had just opened, so everything in the room was fresh and new. The room was much larger and it was about a one minute walk to the beach. I had a nice, clear view of Diamond Head from my room. Some of the rooms may have water views. I used Hyatt GP points for the stay and if I recall correctly I used 12,000 points a night. So it was very worth it.

When checking in at both properties ask the front desk agent if they can get you onto a high floor with a view. They may be able to do something for you.

You may also want to think about taxiing to/from the airport and just renting a car when needed since you'll be paying at least $25 a night for parking at the hotels. There are many options to rent cars in Waikiki and I've found the rates to be the same or cheaper than the airport rates. I usually do price comparisons on Kayak and decide.

Go to the house without a key at the Halekulani to listen to live Hawaiian music and have a drink and watch the sunset one evening.

The Outrigger Reef also has live Hawaiian music playing every evening as well. The Shorebird restaurant at the Outrigger Reef is a great place to grab a beer and watch the sunset as well.

Look into Uber it was just catching on when I was last there in August. The UberX cars may be coming and going to/from the airport now. I used them for local rides if a car was close by and it worked out great.