Ithaca NY has Ithaca Falls in the city.
True, but I think the OP was asking about natural wonders.
A borderline case in this regard would be Panama City, located at one of the ends of the Panama Canal. It’s a man-made waterway, of course, but cutting through scenic nature.
Good point.
It’s like 50 miles from Mt. Rushmore though. Otherwise there’s not much particularly wondrous or landmark-ish near there, except maybe that giant pit in Lead. Custer is a nicer little town with better restaurants that’s just as smack-dab in the middle of the Black Hills.
That’s got to be the front-runner for “natural wonder right in the city”. I was astounded to come around a corner and see a giant brass plaque stating it’s city park status.
“Landmark” may be stretching it, but the Alamo is located smack dab in the middle of downtown San Antonio. I was expecting it to be on the outskirts.
Well, there’s Cairo…
https://sacredsites.com/images/africa/egypt/great_pyramid_at_dawn_1200.jpg
Mt Shasta City, CA…Mt Shasta is the 11th most prominent peak in the US (including Alaska) rising ~10,000 feet above the surrounding area…
Don’t go looking for the basement – you ain’t finding it!
Dubious, at best: Baltimore’s “Red Light” district (“The Block”) is directly across the street from City Hall. Make of it what you will.
Edinburgh has this thing right in the middle of it:
Also Arthur’s Seat on the edge of town:
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Minnehaha Park in Minneapolis Minnesota has a 53-foot waterfall:
Minnehaha Falls and Park: Planning Your Visit (tripsavvy.com)
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Hangzhou is centered around West Lake (Xihu). Nanjing has Purple (Zijin) Mountain. Hong Kong island has Victoria Peak.
It has two basements now.
They cheated! 
Mount Fuji is pretty darn close to Tokyo
Popocatépetl is just outside of Mexico City.
Colorado National Monument, Book Cliffs and the Grand Mesa near Grand Junction.
Rochester, NY, was built around the Genesee River, and a series of mills connected to multiple waterfalls made it the country’s preeminent wheat milling center for a while. The falls are now somewhat tamed but still are near the center of downtown. The Upper Falls has an observation bridge to view it from.
The Lower Falls is prettier and wilder.
Well, let’s see what’s on that list.
Grand Canyon village, I guess. It’s got 1700 or so folks who actually live there.
North Rim is pretty tiny, closes down from December 1 to mid May, and has no permanent population.
Supai is sort of close, has 200 residents, but it’s still a looong walk from Supai to the canyon, 17 miles
That’s all I can come up with.
Well, a tick disease specialist probably wouldn’t make much of a living in a place without many ticks . . .
Mount Royal is smack dab in the middle of Montreal.