Good availability for intra-Japan award flights for 7,500 AAdvantage miles each way in Economy, with
no cash component. (Higher redemption rates for Business and First, when available.) AAdvantage awards are fully refundable with no fee if cancelled prior to scheduled departure time.
But as another poster noted, if you can get a cheap cash fare and can live with the fare's conditions, then a mileage card might not be the best solution for you.
If interested in AA miles, look at the Citi AAdvantage Platinum Select card, and the Citi Strata Premier card. Note that spend on the Citi AAdvantage card earns AA Loyalty Points which count towards attaining AAdvantage elite status.