Compiled from various sources:

• Air traffic controllers and TSA officers are supposed to be working, but aren't getting paid, so actual on-the-job staffing may be thin.
• State Department says it continues to process passports and visas.
• Embassies and consulates abroad are open.
• Trusted Traveler Programs are essentially on hold.
• Smithsonian buildings in DC are closed.
• National Zoo in DC is closed.
• National Parks, memorials, battlefields, trails, seashores: mostly open (but subject to change) - but maybe without restroom facilities Inquire ahead at NPS.gov.

Federal employees not receiving paychecks is of course affecting demand for tourism also.