I visit TYO from LAX at least once a year, and just about every trip has TYO on a lengthy stopover (often longer than my time at the final destination). I usually book LAX-TYO-HKG on NH for $400-500 RT, but I have also booked to LAX-TYO/KIX-SIN for $300 on JL. The key is that NH airfare is almost always much lower when booked code-share via UA. I used to always get exit row seats for that price, but now NH is charging extra for seat assignments like JL and most other airlines. Adding a side trip to HK or SIN is just icing on the cake for me (especially when I get to combine Tokyo Disney & HK Disney, as I have a sickness).

The only airline that ever really has a sale on LAX-TYO is Singapore, since it is a layover stop at NRT on one of the LAX-SIN routes. MH used to compete on this route as well before they pulled out of LAX.