Fly the ocean in a silver planeThis turns out to be correctly recalled; it comes from the 1952 You Belong To Me. Here's the Jason Wade cover:
See the jungle when it''s wet with rain.
Those faraway placesThis Google finds - the tune also identifies it - to be misremembered lyrics of the 1948 Far Away Places:
Where elephants roam
Those faraway placesHere's the 1961 Sam Cooke cover:
With strange soundin' names
I never see the morning bright,This one is baffling me.
I sleep all day and dance all night.
I know that it's wrong, but it's swell.