The gargantuan Golden Gate Park – celebrating its 150th anniversary this year – is actually 20% bigger than Central Park in New York, and it's got all the charm and attractions of its East Coast counterpart. Stroll through the entrance for free and drink in the park's lakes, landmark windmills and its famed bison herd. The teetering Hamon Observation Tower is also free, offering 360° vistas from 144 feet (44m).

The perfect stop for book-loving visitors to the capital, the vast Library of Congress spreads itself over three buildings: the John Adams Building, the James Madison Memorial Building and the Thomas Jefferson Building, all on the iconic Capitol Hill. The latter is the most impressive site of all, with intricate gilding, grand columns and arches and frescoes. Then there's the books: the library holds 164 million tomes, documents and other relics, making it the largest library in the world. All three buildings are free to enter. Here are more of the world's most incredible libraries.

You can't visit the Bluegrass State without sampling some of its finest whiskey, and the Buffalo Trace Distillery in Frankfort, designated a National Historic Landmark, is one of the top places to do so. Come by for the complimentary Trace Tour, which chronicles the history of this legendary distillery and also offers the chance to wander through barrel-packed warehouses. True spirit nerds should alternatively opt for the Hard Hat Tour (also free), which gets into the detail of the bourbon-making process. All tours come with a tasting too.

Now a designated marine sanctuary, this eerie tangle of abandoned ships is dubbed the largest shipwreck fleet in the Western Hemisphere. The vessels date to the First World War, when hundreds of wooden steamships were built – the ships, which were poorly constructed in haste, ultimately never made it to war in any capacity, and were eventually deserted in Mallows Bay. Today they remain, haunting and decaying, a habitat for osprey and a fascinating attraction for kayakers in the bay. See more stunning photos of the world's most spectacular shipwrecks here.

It's completely free to wander down this street in the Motor City's East Side and drink in the weird and wonderful works by artist Tyree Guyton. Guyton, who is often spotted tending to his curious creations, embodies the saying 'one man's trash is another man's treasure'. He warps sculptures and scenes from materials that have been found and visitors can expect to see houses emblazoned with polka dots, rainbow-faced clocks and structures made from dolls, stuffed animals, shoes and car parts.  

Yes, there is an entire museum dedicated to SPAM® in the southeastern Minnesota town of Austin. The institution is a loud, proud celebration of the canned meat, which was first invented back in the 1930s. You'll learn all about the history of SPAM®, including its key role in the diets of troops during the Second World War, and pore over a huge store of SPAM® memorabilia. Free guided tours are available over the weekend and upon request. See more of America's wackiest museums here.

The southwest has little shortage of haunting ghost towns, and this creaking abandoned settlement in southern Nevada is a great example. The mining town of Rhyolite mushroomed in the early 20th century and was soon complete with shops, a jail, an impressive bank building and homes for the workers. By 1916, though, the town had been deserted, and today crumbling remnants are all that remain. Step back in time and take a wander between the structures: the train depot and the mercantile are particularly impressive. Check out the eeriest ghost towns in America.

No trip to the Big Apple is complete without visiting the green heart of the city. Central Park covers 843 acres of Manhattan and is free for the public to enjoy all year round. As well as the grounds themselves there are regular (free) open-air shows and even some complimentary guided tours put on by the Central Park Conservancy. Discover what else the city offers with our comprehensive New York guide. 

"The Topiary Park is a landscape of a painting of a landscape" – that's how this gallery-cum-garden was described by its creator, local sculptor James T. Mason. It's dotted with all manner of leafy creations, and is intended to be a recreation of the painting A Sunday Afternoon on the Island of La Grande Jatte by Georges Seurat. Orient yourself in the visitor centre before heading out to explore Mason's green-fingered work. 

The mammoth rock carvings of Mount Rushmore attract millions of visitors per year, and entry to the park is free. George Washington, Thomas Jefferson, Theodore Roosevelt and Abraham Lincoln have peered out from this cliff face since 1941, each selected for their great impact on America's history and progression. The Presidential Trail, circling the monument, offers great views. Discover the hidden secrets of the world's most famous buildings.

There's a reason Nashville is touted as "Music City": you're never far away from the sound of country or blues or rock 'n' roll, and nowhere is this truer than along neon-drenched Lower Broadway. Though you'll probably want to buy a beer, there's no cover charge for the bars and honky tonks along this fabled street, where you'll find live music every night. If you don't want to spend a single dollar, wandering along the boulevard, listening to the music pouring from the venues, is completely free.

There's no charge to soak in the skyline of downtown Knoxville from the observation deck of this striking structure. The Sunsphere, crowned with its eye-catching golden ball, was designed back in the 1980s for the 1982 World's Fair, and it still stands tall at a whopping 266 feet (81m). Make your way up for 360° views of the city and displays and photographs documenting the history of Knoxville. 

This mission in San Antonio is famous as the site of the 1836 Battle of the Alamo. Here Texans clashed with invading Mexicans during the Texas revolution, in a cross swords that would last almost two weeks. Today it's a preserved historic site and education centre, bringing to life this pivotal battle, and remains one of the most-visited attractions in the state. 

Here's 5 reasons why San Antonio should be on your wish list

Beautiful North Cascades – with its lakes, glaciers, mountains and dense forestland – is one of the most underrated sites in the national park system, and among the 10 least visited. When you consider the fact that the park is entirely free, this fact becomes all the more mystifying. You can experience this unspoilt wilderness on myriad trails, which range from straightforward hikes (the Bridge Creek Trail) to much more strenuous and challenging undertakings (the Sourdough Mountain Trail). Pictured is Diablo Lake, in the Ross Lake National Recreation Area. 

With its bold rotunda and elegant whitewashed façade, this is one of America's most beautiful capitol buildings. The architect, Ohio native Cass Gilbert, also worked on some of the nation's earliest skyscrapers, including New York City's Woolworth Building. It holds a spot on the National Register of Historic Places, and free tours of its interior can be arranged. Read about America's most historic attractions from every decade.

This intriguing museum belongs to the University of Wisconsin, but remains dedicated to educating the public. With roots dating right back to 1848, the museum has now gathered more than 120,000 specimens, including an impressive store of dinosaur fossils. Self-guided tours are free, but if you want an expert to show you around, you'll need to pay $2. Take a look at 34 of America's most important landmarks.

To really get to grips with Wyoming, you'll need to venture outdoors, and this site is both a natural and historic wonder. Castle Gardens, in the state's centre, is famed for its petroglyphs – free to explore, the area boasts detailed rock art thought to date back to around AD 1000, mostly depicting armed warriors. It's a somewhat rocky and remote drive out here, but it's worth it for such a wholesome dose of history. Now discover the best theme parks in America.