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Hundreds of tourists, including New York's Debbie Turczan and her family, expected to spend Tuesday hiking in Yellowstone National Park.
On the second day of the Turczans' five-day vacation—and the first day of the government shutdown that has closed the National Park Service's parks and landmarks—the family is searching for a new plan.
"I called the park this morning and was told they were following instructions to start closing as of 8 a.m.," Turczan said in an email. "We are looking for other hikes to do, but it is a challenge because many of them cross onto national park or forest land."
"We are so very disappointed," she said. "We waited six months for this trip."
(Read more: Shutdown could trigger 'Fed flare': Trader)
Tourists nationwide find themselves in similar fixes, with attractions such as the Statue of Liberty, the Liberty Bell Center and the Smithsonian museums all closed.
"We've had lots of people coming up and pulling on locked doors," said James Cuorato, the president and CEO of Independence Visitor Center in Philadelphia. "It's very, very frustrating."
Although there's no substitute for seeing Old Faithful or the National Zoo's pandas in person, experts say people aren't entirely out of luck.
"Many of these landmark attractions are in cities that lend themselves to major tourism activities," said Gabe Saglie, a senior editor at Travelzoo. Privately operated and state-run attractions remain open, and local tourism boards can direct travelers to alternatives that fit their interests.
In Philadelphia, open attractions include the National Constitution Center and the Betsy Ross House, Cuorato said. In Washington, the National Geographic Museum waived its admission fees of up to $11 on Tuesday.
Things are tougher for those heading for a national park.
"Those are often destinations in and of themselves," said Anne Banas, executive editor for SmarterTravel.com. Visitors who had planned to camp in the parks will also need to find other accommodation, as campgrounds are closed as well.
Robin Hoover, executive director of Yellowstone Country Montana, said nearby state parks are a possibility for displaced visitors looking for camping spots and outdoor activities.
"You can see a lot of the same kinds of scenery, minus the geothermal features that are unique to Yellowstone," she said.
Because it's unclear how long the shutdown might last, people with upcoming trips may want to consider their plans, said Saglie, adding, "We're in this wait-and-see approach."
Travelers have some leeway to change their arrangements—for a price.
Hotels allow penalty-free cancellation with as little as 24 hours' notice, Banas said. Changing an airline ticket can cost, though, with many major carriers charging $200 on domestic routes, plus the fare difference. (If closures have derailed your trip, she advised that you ask the carrier to waive that fee. You never know.)
If you bought trip insurance, ask if attraction closures are a covered reason to cancel, said Linda Kundell, a spokeswoman for the U.S. Travel Insurance Association. It's usually not, with the exception of "cancel for any reason" policies.
For some travelers, however, canceling isn't an option.
Rather than pay $600 to change her flight, Anne Ju of Ithaca, N.Y., will fly to Montana on Wednesday to visit Yellowstone and Jackson Hole, Wyo., en route to Seattle—a trip she's been thinking about for years.
"I could cancel, but it would be expensive, and I took time off to do this," she said. "I'm just going to go and see what happens."
—By CNBC's Kelli B. Grant. Follow her on Twitter@kelligrant.