Citibank Hilton HHonors Visa

No annual fee. Earns 2 HHonors points per $1 spend. Points convert to ANA miles at 10:1, so your net earn rate is a mere 0.2 miles per dollar, but hey, it's fee-free.

Citi also has a fee-free "Bronze" AAdvantage credit card which earns 0.5 miles per dollar, but they don't offer it on their web site. I got it issued over the phone by cancelling a Platinum card, stating that I didn't want to pay the fee. The representative changed me over to the fee-free card on the spot.