(This article originally appeared o the Wall Street Journal online)

The New York Stock Exchange was once a tourist mecca. From 1939 until roughly 15 years ago, crowds arrived daily for a glimpse of the bustling trading floor.

But since the morning of Sept. 11, 2001, the building and its exchange have been closed to the general public—much to the dismay of many first-time visitors to New York. Though the NYSE, part of Intercontinental Exchange Inc., ICE -0.46 % did consider reopening to the public at one point, a spokeswoman says it has no plans to do so in the immediate future.

The long closure has ended not only an option for tourists, but a chapter of Wall Street history. Gone are the days, for example, when anarchist Abbie Hoffman could walk up to the visitors area as he did in August 1967 and throw dollar bills to the trading floor below—in what Mr. Hoffman described as a rebuke to capitalism. (Three months later, the exchange installed bulletproof glass in the visitors gallery.)

Visitors can still enter the stock exchange if they can find an exchange member willing to sponsor their visit. According to a memo outlining the NYSE’s rules of conduct, visitors must be at least 14 years old and on their best behavior. (The memo spells out hefty fines for traders who commit decorum infractions, including “consensual rough play or kidding around,” “use of artificial noisemakers,” “practical jokes” and “running.” Fireworks are also “strictly prohibited.”)

Without an invitation, tourists have to make do with a view of the NYSE’s neoclassical facade—from beyond the black metal gate that wraps around the building’s perimeter.

Visitors will find no warmer a welcome at New York’s other famous stock venue: The Nasdaq Stock Market NDAQ -0.96 % ’s building in Times Square isn’t open to the general public either.

So where is a Wall Street-obsessed tourist visiting New York City to turn? There are several possible destinations.

One is the Museum of American Finance, at 48 Wall St. Formerly a one-room gallery in the Standard Oil Building, a few blocks away, the museum moved in 2008 to accommodate more tourists, a spokeswoman says. The finance museum currently is showing an exhibit featuring the way gold influences our lives.

Speaking of gold, the Federal Reserve Bank of New York is also in the neighborhood and offers guided tours. Learning about monetary policy is no Disney ride, but visitors may get a charge out of seeing the heavily guarded gold vault. In 2015, according to the bank’s website, the vault stored about 508,000 ingots, weighing about 6,350 tons.

For those who like to walk, another possibility is the Wall Street Experience, a tour company that rarely takes clients inside any buildings—except, occasionally, Federal Hall, where George Washington was inaugurated, a stone’s throw from the NYSE. The tours instead offer insider perspectives of the financial industry, with historical asides.

Some say that tourists aren’t missing that much by the NYSE not reopening its doors. Trading today is a less-theatrical affair, notes Andrew Luan, founder of the Wall Street Experience and a former Deutsche Bank trader. The popular image of wildly gesticulating floor brokers shouting bids “is a relic of how things used to be done,” he says.

For a more tactile Wall Street experience, the curious often visit the “Charging Bull” sculpture in the park at Bowling Green. The bull’s large brass testicles figure prominently in many a photo souvenir.

“I’ve heard it gives you luck with the money,” a Russian visitor says, standing beside the bull, her camera phone at the ready.