Welcome to FT.

According to the Mileage Converter at webflyer.com, the best way to do it is through the Diners Club program (which requires actually having a DC card), which would turn 20,000 AA miles into 10,000 DL miles. If you don't have one, then the best way is through the Hilton HHonors program, which would turn the 20k AA miles into 4,000 DL miles. (Suffice it to say that there is no way to do it without losing value.)

I'd also note that any activity will keep the AA miles intact -- even if you spend a few dollars through the eShopping site -- which might be a better way to go (that is, save the miles until you get enough to use them). Another option worth considering is simply to transfer them to Hilton HHonors -- for $25, you'd have enough points to stay at just about any Hilton in the world for one night.

Mike