The following site has VERY FEW properties listed, but they offer a sort of reimbursement, for staying at their property, in cash-back or credit but not in miles.

http://www.frequentdrivermiles.com/


Here is a quoted excerpt from their site:
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Here is what most [hotel properties] are doing:

Reimbursing you for a gas receipt dated the day you arrive (They buy your gas)

Offering a set mileage credit from your location as a credit to your bill

Some hotels are offering you the option of exciting upgrades as well. For instance, one member property will offer you 150% of your gas mileage credit towards a meal in their award winning dining room! Another pays for your return trip for a two-night stay. Reasonable limits apply and there are blackouts for periods of high demand.

Finally

Thanks for being part of an excellent cause. These hotels have not asked for, nor do they expect, a Federal bailout. They are willing to earn your dollars, provide friendly service, and contribute to our society. Now, that’s American!
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Got points ? Got smiles !