When I think back about going to China, Thailand, Japan, Russia, and
various U.S. places (NYC, Washington D.C., Florida, Oregon, San Juan
Islands), the best part of each vacation always seemed to be the
bicycling part.

The bicycle route through Manhattan is awesome, as is the bicycle trail
from Alexandria VA to Mount Vernon. The Shark Valley Trail in the
Everglades is famous not for sharks, but for the alligators that sun
themselves on the trail (those aren't speed bumps, steer around them not
over them).