AA and some other airlines have a program where they will recommend a dealer and you get 1 mile for every $4 purchase. As I wasn't needing to finance and the rate WASN'T good for a Toyota Prius I shopped around and found a dealer that WAS willing to let me use my credit card for the TOTAL purchase (on AMEX for me). Tried other dealer in the Chicago area and the others were willing for only about $2K. If I had wanted to finance, I would have gone with the first dealer where I would have gotten miles. I got more miles this way. Once you definitely know what you want you could try walking in and asking right away if they accept a credit card for full purchase - then you are not wasting your time.
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DtG