What cities have a natural wonder or landmark right in the city or at least adjacent to it? I am talking about a canyon, waterfall, rock arch, mesa, cavern or something spectacular that people might travel to come see. The only one I can think of in the US is Niagara Falls. It seems that most natural wonders are far from population centers. I think that it would be fair to exclude rivers, lakes, and shorelines since so many cities are built next to those (unless you know of a spectacular exception). This question was inspired by my son who asked why we always have to travel so far from “civilization” to see something naturally spectacular.
Ronda, Spain, I think qualifies:
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Rio De Janeiro has Sugarloaf Mountain:
Cape Town sits at the foot of Table Mountain, which is a 1,000 meter (3,500 foot) mesa.
Vernal, Utah is basically right next to Dinosaur National Monument.
Arenal, Costa Rica has Arenal Volcano looming over it.
San Francisco is very close to Muir Woods.
Deadwood SD is located in a gulch that is part of the Black Hills National Forest, home of Mt Rushmore.
Garden of the Gods is a city park in Colorado Springs.
The La Brea Tar pits are a mile away from downtown Los Angeles.
And Pikes Peak is about 5 miles from Colorado Springs
Beaten to it 
You can, of course, see Mount Fuji from Tokyo.
So not a city. Might as well list every village along the Grand Canyon.
Odessa, Texas has the Meteor Crater. Mrs. J. stopped there on her travels, and got me a t-shirt.
Woodruff, Wisconsin has what’s billed as the World’s Largest Penny (not a natural wonder, but certainly a landmark).
They’re currently advertising for a tick disease specialist there. Must be a great place to live.
Huntsville, Alabama, was founded around “Big Spring.”
Duluth, MN is on the shore of Lake Superior, which I think can be considered a natural wonder.
Naples, in Italy, sits under the still-very-much-alive volcano of Versuvius
A little less dramatic, but my own humble home town of Bristol, SW England, is famed (at least here) for the Avon Gorge and Clifton suspension bridge, about 15 mins walk from the city centre.
San Francisco obviously. Golden Gate…
And less well known Lands End:
Though having moved from SF to DC, I’m surprised by the number of trails here in DC. None of them are quite up to SF standards in terms of natural wonder, but the C+O canal by Georgetown is getting there (and they are far more accessible to downtown DC, and the less well off suburbs, than anything around SF) :
And Rock Creek:
Gibraltar is not particularly big, but it has the absolutely spectacular St. Michael’s Cave essentially right underneath it (inside the Rock of Gibraltar, which is quite scenic in its own right)
http://www.visitgibraltar.gi/uploads/Attractions/Lower%20St%20Michaels%20Cave.jpg
But Deadwood is not along the edge of the Black Hills, but to your point its actually a town (not a city) surrounded by the Black Hills National Forest which includes Mt. Rushmore. It just seems like a city when all the tourist are there.
Ocala, Florida, has Silver Springs where they filmed, “Creature From The Black Lagoon,” among other things.
Giza (Cairo) has some pyramids.