"I've never seen a space shuttle, and I'm looking at one," said Thomas Hoffler, 69, who described himself as homeless. "I'm just spellbound.
Fashion photographer Stewart Shining, 47, said his young nephews in California had emailed him to ask if he could see the Enterprise.
"I just walked over and had a peep and took some pictures," he said.
Multimedia producer Tara Gore also took a break from work to watch the shuttle.
"There's so much going on in New York that you can walk out of your office and see the space shuttle floating by," she said.
The Enterprise's original move-in date was Tuesday. Organizers said Monday that bad weather had delayed preparation work.
The shuttle was towed to New Jersey from Kennedy Airport on Sunday.
A spokeswoman for the Intrepid said the shuttle's wingtip sustained light cosmetic damage during the Sunday trip when a gust of wind caused it to graze a wood piling.
The Enterprise never went on an actual space mission; it was a full-scale test vehicle used for flights in the atmosphere and experiments on the ground.
It comes to New York as part of NASA's decision to end the shuttle program after 30 years. It is scheduled to open to the public in mid-July.
Many who watched the shuttle's passage up the Hudson posted photos on Twitter.
Maricel Presilla, a food writer, tweeted, "WOW. Space shuttle passes by the Hudson on its way to Intrepid. Big deal to see it on the water."