Travel has the connotation of a distance. For instance, when people say they enjoy traveling, they don't mean going to the grocery store. Rather they mean other countries, distant cities cities, etc.
Go (to go) is a pretty generic term for any kind of moving about. "I'm going to the store." "I'm going upstairs." "I'm going across the street." "I'm going to work." "I'm going to Florida this summer." "I'm going home at 6 PM" As you can see, it can be used in almost any case.
Walking is moving by foot. You walk on the sidewalk. You walk up stairs. This is a distinction between other forms of travel. For instance, some people drive to work and other people walk to work.