Saigon's one million motorbikes don't make for calm explorations, but you can escape the fray at the 130-year-old Saigon Zoo and Botanical Gardens. Wander the vast green park with its bonsai trees and orchid collection, and check out elephants and tigers in the zoo.
The War Remnants Museum in District 3 has immaculate tanks and planes outside, as well as sobering exhibits detailing the realities of the war. Note it's closed for an hour and a half starting at noon. Outside town, visit the Cu Chi Tunnels to learn how the Viet Cong moved underground.