I know we're asking the impossible here, but we're looking for an AWD sedan, not an SUV, with high gas mileage. Any recommendations?

I have a 2004 Volvo S80 AWD (2.5 Turbo engine). On a trip I can easily get 30MPG cruising at the speed limit (up to 70MPH). Around town (suburban environment) I can consistently get 21-22 MPG. Both mileages are in the spring, summer, and fall - mileage in the winter is lower. Lots of room and comfortable. Don't know if you consider this high mileage or not. FWIW, the legendary safety of the Volvo makes it "best" for me. YMMV.

Thanks--that's very helpful!! Yes, 30 mpg is fairly high to me, although when they put out the first Prius AWD I'll be right there ready to buy! Thanks again.

Supposedly the FFH (Ford Fusion Hybrid) is to come out next year; though I personally doubt it due to a lack of information lately. Since they advertise the Fusion currently as a great AWD sedan, you may want to think about that.

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Have you read the FEH FAQ?

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It seems like a 4cyl non-turbo Subaru would be what you're looking for. A Ford Fusion or Five Hundred AWD may come close.
If you're open to wagons, there's also the Toyota Matrix 4WD, Suzuki SX4, and even the Mercedes R320 diesel.