The capital city of Austin is located in the Texas Hill Country and has long been noted for its many hills (or mounds). By at least 1841, Austin was called “City of the Hills.” The slightly shorter nickname “City of Hills” is cited in print from at least 1854.
 
A similar Austin nickname in the 1840s was “City of a Thousand Mounds.”
   
   
Wikipedia: Austin, Texas
Austin is the capital of the U.S. state of Texas and the county seat of Travis County. Located in Central Texas on the eastern edge of the American Southwest, it is the fourth-largest city in Texas and the 15th-largest in the United States. It was the third-fastest-growing large city in the nation from 2000 to 2006. According to the 2009 U.S. Census estimate, Austin had a population of 757,688. The city is the cultural and economic center of the Austin–Round Rock Metropolitan Area, with a population of 1,652,602 as of the July 2008 U.S. Census estimate—making it the 36th-largest- and 2nd-fastest-growing metropolitan area in the nation.
 
The area was settled in the 1830s on the banks of the Colorado River by pioneers who named the village Waterloo. In 1839, Waterloo was chosen to become the capital of the newly independent Republic of Texas. The city was renamed after Stephen F. Austin, known as the father of Texas. The city grew throughout the 19th century and became a center for government and education with the construction of the Texas State Capitol and the University of Texas. After a lull in growth from the Great Depression, Austin resumed its development into a major city and emerged as a center for technology and business. Today, Austin is home to many companies, high-tech and otherwise, including three Fortune 500 corporations, Dell, Whole Foods Market, and Freescale Semiconductor.
 
Austin was selected as the No. 2 Best Big City in “Best Places to Live” by Money magazine in 2006, and No. 3 in 2009, also the “Greenest City in America” by MSN. According to CNN Headline News and Travel & Leisure magazine, Austin ranks No. 2 on the list of cities with the best people, referring to the personalities and attributes of the citizens. Austin was also voted America’s #1 College Town by the Travel Channel. Austin was ranked the fifth-safest city in part because there are fewer than 3 murders per 100,000 people annually.
 
Residents of Austin are known as “Austinites” and include a diverse mix of university professors, students, politicians, musicians, state employees, high-tech workers, blue-collar workers, and white-collar workers. The main campus of the University of Texas is located in Austin. The city is home to enough large sites of major technology corporations to have earned it the nickname “Silicon Hills.” Austin’s official slogan promotes the city as “The Live Music Capital of the World,” a reference to its status as home to many musicians and music venues. In recent years, many Austinites have also adopted the unofficial slogan “Keep Austin Weird”; this refers partly to the eclectic and progressive lifestyle of many Austin residents but is also the slogan for a campaign to preserve smaller local businesses and resist excessive commercialization.
 
Google Books
Southwestern Historical Quarterly
v. 59 - 1956
Pg. 71:
Austin, Nov 22 1841.
Dear Sir—
After a protracted journey of Seven days, I have at last arrived at the City of the Hills, and a dull, dreary looking place it is, to make the most of it.
 
16 November 1844, Sandusky (OH) Clarion, pg. 2, col. 1:
The town of Austin, sometimes called the city of the hills, once the seat of government of the republic of Texas, is situated in a bend of the Colorado river.
   
Google Books
7 September 1848, The Friend, “The Upper Colorado,” pg. 407, col. 2:
To many little is known of the Colorado river, above the “City of the Hills.” (...) Through almost the entire course of the river, the banks are prominent and well defined, until it reaches the City of the Hills, the present capital of the State of Texas.
   
13 February 1854, Texas State Gazette (Austin, TX), pg. 164:
“VOX,” the male Anastasia Pugsly, who, to use his own inimitable language, “aspires ‘to paint the rainbow,’ embellish the clouds, or count the brilliant stars that float and shine in etherial splendor, above, around and through the “city of hills” (Austin—ed.), for the benefit of the readers of the Marshall Meredian, is out in a whole column of interminable sentences, devoted to the demolition of the editor of the Gazette.
     
26 February 1859, Standard (Clarksville, Red River County, TX), pg. 2: 
AUSTIN, TEXAS, January 12th, 1859.
Dear Major:
(...)
Certainly, Venus has bestowed especial favors upon her daughters of the “City of the Hills.”
 
Google Books
May 1859, De Bow’s Review, “The Archive War of Texas,” pg. 523:
Thus the heavy clouds, which had so long lowered over the destiny of Austin, the beautiful “City of the Hills,” were dispelled.
 
3 June 1867, San Antonio (TX) Express, pg. 2:
LETTER FROM AUSTIN.
AUSTIN, TEXAS, May 28, 1867.
Editor Express:—
The little City of Hills, the hot-bed of radicals, is about in status quo.
   
13 August 1868, Galveston (TX) Daily News, pg. 3, col. 1:
I left the fair City of Hills (Austin) on the 22d of July, and after a tiresome ride of forty-one miles towards San Gabriel, night overtook me in the prairie, where I spread my blanket for the night, for the first time, and I retired to my lonely couch.
   
13 March 1871, Union (TX), pg. 2:
Special Austin Correspondence.
AUSTIN, March 8th, 1871.
Messrs. Editor:
(...)
So you see in the fair City of Hills we have many means of killing time, and “shooting folly as it flies.”
 
28 September 1872, Dallas (TX) Weekly Herald, pg. 1:
Rather should her energy amd intelligence work for the retention of the Capital at Austin, and encourage the citizens of the seat of government in every laudable effort to improve and beautify the “City of Hills,” so that in the dead heat of July and August, Houstonians can flock to the hills of Travis for health and recreation, and be proud of the Capital of their State, and feel that part of its beauty and attractions are due the railroad city of the State.
 
Google Books
History of Texas, from its discovery and settlement, with a description of its principal cities and counties, and the agricultural, mineral, and material resources of the state.
By J. M. Morphis
New York, NY: United States Publishing Company
1874
Pg. 510:
It (The city of Austin—ed.) has more hills than the Eternal City, and hence its cognomen City of Hills, high above all of which Mount Bonnell rears its lofty head, looking down with complacent grandeur and dignity upon the sparkling waters of the river at its base.
 
The Portal to Texas History
Indian Wars and Pioneers of Texas
By John Henry Brown
Austin, TX: L. E. Daniell, Publisher
1880
Pg. 740:
Mrs. Whipple was born in Lowndes County, Ala., in 1832, and recalls with feelings of both pleasure and regret the many scenes of her girlhood, incident to the early settlement of her (now beautiful) “city of the hills.” (Austin—ed.)
 
Googel Books
Robert Potter:
Founder of the Texas Navy
by Ernest G. Fischer
Gretna, LA: Pelican Publishing Company
2007
Pg. 188:
The Houston Morning Star already had got in a few blows, such as this from their March 11 (1842—ed.) issue:
   
The way the married ladies in Austin attend balls and parties is a beautiful commentary of the security of “the city of hills.”