Where is your hotel so we can recommend the best pot for you? Some hotels may have valet space out front they would just hold your vehicle. Maybe embassy suites, not the JW Marriott, not the Willard, maybe Westin yes, marquis no..... Just varies on location.

Some options - Outdoor lot between 5th and 6th NW, New York and K Streets - I've never parked there but I'd imagine it's available overnights.

Above ground garage at Giant Food 1300 blk Park Rd NW - no barriers to enter and ramp goes to top level with no overhead obstructions

Howard University pay lot - outdoors, no barriers overhead, 2235 8th St NW