I think I have to agree with PTravel here; unfortunately with Beijing traffic getting to the Hyatt, eating dinner, and getting back to the airport in time to get to the gate, etc, is going to take your whole six hours. I will admit, though, the Duck at the Hyatt might just be worth it. If you imagine Beijing as a (really big!) clock, the airport is outside of 2, but the Hyatt is way down at the 4 or 5 (if memory serves).

I might advise, though, considering you'll be landing right in the heart of rush hour, to take the subway back into the city. If your Chinese is none/limited, cab might be the most reliable option, but if you're daring I think the subway might save you 20-30 minutes at 6:00PM. Heading back to the airport, though, cab should be fine.

Six hours should be plenty, but if I hate to say I would advise against being too greedy and trying to squeeze in something else. Otherwise, enjoy the evening in Beijing!