Nairobi National Park:
“A short drive out of Nairobi’s central business district is the Nairobi National Park. Wide open grass plains and backdrop of the city scrapers, scattered acacia bush play host to a wide variety of wildlife including the endangered black rhino, lions, leopards, cheetahs, hyenas, buffaloes, giraffes and diverse birdlife with over 400 species recorded. Visitors can enjoy the park’s picnic sites, three campsites and the walking trails for hikers.”
As with other cities mentioned, Spokane WA has rapids and falls running through the middle of it.
Of course, from St. Louis down to NOLA the Mississippi River rolls along right past downtown in a bunch of major cities.
That parking lot in Twin Falls Idaho is surreal. You walk out of the front door of Best Buy, Old Navy, or TJ Maxx, walk to your car, and there you are on the edge of the Snake River Canyon.
That’s one big-ass pothole y’got there, son. DPW should be fillin’ that in any day now. 
I am surprised no has mentioned beaches which are the natural wonder most commonly found in a city. Among big cities, Rio and LA possibly have the best beaches. If you add in Sugar Loaf Mountain, mentioned above, I think Rio may be the winner for the major city with the most spectacular natural attractions.
OK. I see the OP said no shoreline which I suppose would exclude beaches though I would imagine the Rio beaches in particular would qualify for the “spectacular exception”.
Well, North and South Tahoe, for sure. lake tahoe - Bing images
Man, that used to be a long drive from town. And the loop was not patrolled at all. Good times on a fast motorcycle or quick little sportscar. Those days are long gone…
Vegas sprawl sucks.
No kidding! I was there a few weeks ago and Vegas appears to be the offspring of Los Angeles and Phoenix; I was starting to call it “Los Phoenix”. Happily, the weather was nice and snow-capped peaks could be seen west of the metro so it’s possible to see some nature among the miles of strip malls, cinder block walls, and massive freeways.
I did not get out to Red Rock but it appears to be right on the edge of town now.
It was on the outskirts… in 1836.
Speaking of Phoenix, has anyone mentioned Camelback Mountain yet?
And just up the road, natural hot springs in Glenwood Springs, CO.
Cave of the Mounds is just a short drive from Madison, WI.
Bend Oregon has Pilot Butte, which has a viewpoint on top with a pretty great 360-degree view of the area.
Just south of town is Lava Butte, which has even a better view.
Butte, Montana has Big Butte on the northwest horizon.
Tucson has both Saguaro National Parks right next to it. Well, okay, it’s a bit of a drive to the Western Part.
As a resident of Cape Town I may be a little partisan 
but I think our beaches and mountains are at least the equal of Rio’s.
The requirement for a city is smaller than many people think, being only 1000 citizens or more (unless you are in a metropolitan area).
Wikipedia lists the place as a city, though it notes it used to have over 25,000 citizens:
Oh, Cape Town has beaches…virtually perfect beaches.
https://format-com-cld-res.cloudinary.com/image/private/s--tK_klABd--/c_limit,g_center,h_65535,w_2500/fl_keep_iptc.progressive,q_95/v1/b7724ab809142bb70582ad7b46948f06/BMDAY2_056_JPG.jpg?1000
(That’s the real beach that is used to represent San Junipero’s in the Black Mirror episode of the same name)
Or we could give them the old two-fer:
Here in the UK we don’t do geothermal, so by local standards a proper hot spring positively stands out as a natural wonder. Impressive enough that the Romans built a big old bath in order to utilize it. Enough of an attraction that a city grew up around it. And what else would you call the city, eh?
j
Just in case anyone doesn’t know: [spoiler]https://en.wikipedia.org/wiki/Bath,_Somerset[/spoiler]
If you zoom in on the street view, that little pile of dirt in the distance in the aforementioned Evel Knievel jump site. That’s a real happening parking lot.
