Washington DC and New York share the same timezone year-round. When it's 12:00 PM in New York, it's also 12:00 PM in DC. Both cities observe DST on the same schedule.
Both cities use Eastern Time (EST/EDT, UTC-5/-4). The entire Northeast Corridor from Boston to Washington shares this timezone.
Any time works! The Amtrak Acela connects DC and NYC in about 2.5 hours. The shuttle flights take only 1 hour, making same-day trips routine.
DC is the US capital and home to federal government, while New York is the financial capital. Many lobbying firms, law firms, and corporations have offices in both cities.