New York’s big-name cultural institutions have no shortage of intriguing exhibition options to choose from, but for something a little more off the beaten path, there’s Museum.

Tucked in an abandoned freight elevator in an alley on the edge of Manhattan’s Tribeca neighbourhood, this quirky venue that showcases obscure, under-the-radar and otherwise uncelebrated objects opens its second season with a reception on 22 February from 6:30 pm to 8:30 pm.

The curated collections and individual items on view run the gamut from random to inventive to obsessive. Sourced from private collectors and Museum’s permanent assemblage, this season features 15 new, exhibits including a sampling of damaged and counterfeit currency and packets of crisps in surf-and-turf themed flavours, such as prawn cocktail and garlic steak. A few exhibitions from the inaugural 2012 season can also be seen, including toothpaste tubes from around the world and a shoe billed as the one thrown at former US president George W Bush by Iraqi journalist Muntadar al-Zaidi at a press conference in 2008.  

In a one-man’s-trash-is-another-man’s-treasure fashion, the mundane is elevated to inspirational, thanks to the back stories of the 175-odd pieces told in the museum’s brochure. Visitors can also access an audio guide by calling a toll-free hotline (888-763-8839) from their mobile phone and punching in the number associated with each item on display.

“We want to remind people of the incredibleness of what we [humans] are, what we make, what we collect,” said Alex Kalman, one of museum’s three founders. “We take pride in seeing meaning [in] and creating a narrative for those things.”

Discovering the 80sqft museum amid the loading docks, fire escapes and shadows is part of the experience. “Like the objects, we wanted the space to be something hard to find,” Kalman said.

In proper museum style, and in spite of its miniature footprint, Museum has squeezed in an espresso machine and a gift shop, offering visitors refreshments and the chance to take home artefacts of their own.

And for those who already have shoeboxes of eccentric finds or overlooked everyday items that are ready for their moment of fame, Museum welcomes submissions for review by the curatorial staff.

Located on Cortland Alley between Franklin and White Streets, Museum is open on Saturdays and Sundays from 11 am to 7 pm through June, although three windows allow for 24-hour viewing of the space from outside.

Amy Brader is the New York City Localite for BBC Travel.