Thomas Stevens rode a penny-farthing bicycle west-to-east around the world in 1884-86, followed by Frank Lenz's east-to-west attempt on a two-wheeled bicycle in the early 1890's -
http://en.wikipedia.org/wiki/Thomas_Stevens_(cyclist)
http://en.wikipedia.org/wiki/Frank_Lenz_(cyclist)
Journalist Nellie Bly held the world record for fastest time in 1890, traveling the world unchaperoned in 72 days http://en.wikipedia.org/wiki/Nellie_Bly