LAX and SFO have the most flights right now. I booked United Polaris award flights LAX->HND and back a couple of months ago, there are saver rates available but you have to be open to certain days.
I ended up deciding to leave a day later and found a United flight operated by ANA in Premium Economy for $1300 one way. I snagged that up and cancelled my outbound points reservation.
I'm going at the end of golden week so things were still busy. If you are looking for award flights try Denver as well since it's not as common of a search as LAX/SFO.