The Acela and Northeast Regional leave from South Station and stop at Back Bay and Route 128, so board wherever is closest to home. Both pull into Moynihan Train Hall at Penn Station.
Flying instead? JetBlue is Logan's largest carrier, and several airlines fly nonstop to New York and to Reagan National.
No car? The Silver Line SL1 runs between every Logan terminal and South Station, free from the airport side, and a free shuttle bus links the terminals to the Blue Line's Airport station. Logan Express buses run from Back Bay, Braintree, Framingham, Woburn and Danvers.
October in New York runs a couple of degrees warmer than Boston: highs in the 60s, cooler nights, so pack layers. May in D.C. runs about ten degrees warmer than home: highs in the mid 70s, lows near 60, a few rainy days. Lighter clothes, plus a rain layer.
And Boston's own leaves usually peak mid to late October, so the New York trip lands right around color season at home.