Tyson's Corner is not a bad place in Northern Virginia. You will find a new Orange Line stop not far from that hotel that will take you to Washington DC monuments in about 25 minutes. I agree the traffic to/from IAD can be dicey.
Tyson's Corner does have some nice restaurants and shopping too. Visited a mate in that area a few months ago.
Sorry, but that layover time sounds exhausting after that flight time. Good luck with that!
For comparison, you should find out where your Qatar 777 counterparts stay. Same area or in DC proper? Similar layover time? Do they get 24 or 48 hours? Fall in the DC area should be lovely....