2 March 2016 Last updated at 15:49 GMT
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Now that they're back home they'll take part in studies to learn about the effects of spaceflight on the body.
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After the show, a cast member thanked Mr Pence for attending and read a letter to him on stage.
"We, sir, are the diverse America who are alarmed and anxious that your new administration will not protect us," Brandon Dixon said.
The incident has angered President-elect Donald Trump, who has accused the cast of "harassing" his running mate.
The President-elect has gone as far as to demand an apology to a "very good man", apparently misunderstanding that the cast implored the audience to stop booing Mr Pence.
"Our wonderful future V.P. Mike Pence was harassed last night at the theater by the cast of Hamilton, cameras blazing. This should not happen!" Mr Trump tweeted.
"The theater must always be a safe and special place. The cast of Hamilton was very rude last night to a very good man, Mike Pence. Apologize!"
His tweet did not go unnoticed by Mr Dixon, who immediately stepped in to defend his castmates.
"@realDonaldTrump conversation is not harassment sir," he wrote. "And I appreciate @mike_pence for stopping to listen."
Mr Pence was loudly booed as he entered the theatre. Audience members said the performance was repeatedly stopped because of jeers.
However, the message, which was reportedly penned by the show's writers when they learned that Mr Pence planned to attend, was greeted with cheers from the audience at the Richard Rogers Theatre in New York.
An audience member tweeted to say there was a three-minute standing ovation when one character performed a song directly to Mr Pence which included the lyrics: "A small query for you / What comes next? / You've been freed / Do you know how hard it is to lead?"
When Mr Dixon addressed theatregoers at the end, he urged them not to boo and asked Mr Pence, who was leaving, to stay and listen.
"You know, we had a guest in the audience this evening, and Vice-President-elect Pence, I see you are walking out but I hope you will hear us.
"There's nothing to boo here, ladies and gentlemen... We have a message for you, sir, and we hope you will hear us out."
Mr Dixon continued: "We truly hope that his show has inspired you to uphold our American values and work on behalf of all of us.
"We truly thank you for sharing this wonderful American story told by a diverse group of men and women of different colours, creeds, and orientations."
A staunch conservative, Mr Pence sparked an outcry earlier this year after signing a law critics said discriminated against the LGBT community by allowing businesses to refuse service over religious beliefs. He later amended the bill.
He is not the first high-profile politician to attend the critically-acclaimed and hugely popular Hamilton, which tells the story of US founding father Alexander Hamilton.
President Barack Obama saw the musical last year and joined the cast backstage after the performance.
Hillary Clinton, who lost to Mr Trump in last week's election, also saw the show. She was supported by its creator, Lin-Manuel Miranda, during her campaign.
Read more: Trump's vice-president-elect: Who is Mike Pence?
The US astronaut Scott Kelly and Russian cosmonaut Mikhail Kornienko have returned to Earth after spending almost a year in space on board the International Space Station.
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US Vice-President-elect Mike Pence was booed on Friday at a performance of the hit musical Hamilton.