The one thing you’ve got right is that you won’t need a car if you live in DC. And busses within DC are free beginning in July and I believe city residents will also get a $100/mo subsidy to use on Metrorail.

Still, a GS-7 is sort of the bare minimum I’d consider for DC (with roommates). You might need to look far outside of the district on a metro line to live a manageable lifestyle.