Welcome to FT, loperfan!
Most flights between Tokyo and the US use Tokyo's other airport, Narita (NRT). The only AA flights from Haneda I can find are AA8401 to SFO operated by Japan Airlines (JL0002) and AA8409 to HNL also operated by JL (JL0080). There are also flights to LAX but they are operated by ANA and Delta, so you won't be able to use AA miles on these flights.
From Narita AA flies to DFW and LAX, and codeshares with JAL to JFK, Chicago, Boston and San Diego.