Right on campus is the surprisingly entertaining Lyndon Baines Johnson Library and Museum, which chronicles the life and legacy of the Texas-born president and is the most visited of all the presidential libraries.
And looming nearby, at the north end of Congress Avenue, is impressive Texas State Capitol, a pink granite edifice four metres taller than its Washington counterpart.
Many Austin visits include a side trip to San Antonio, 127 kilometres to the south. The city of 1.9 million sits at the crossroads of four different ecological zones - Hill Country, Gulf Coast plains, south Texas chaparral and west Texas desert - that together make ideal golf terrain.
First, though, there is the inevitable pilgrimage to the Alamo, the small Spanish mission in San Antonio where in 1836 Davy Crockett, Jim Bowie and other Texas fighters held off a siege by a Mexican army for 13 days.
So rich in history, San Antonio also secured its future and the prosperity of its downtown core with the construction of the River Walk in the 1930s, a miracle of modern urban planning. Rather than paving over the San Antonio River to make room for more buildings, as some developers demanded, the city installed cobblestone walkways along its banks, spanned the narrow river with arched bridges and built steps from numerous street-level locations.
Today, the restaurants, bars and luxury hotels that line its banks along a four-kilometre route make an ideal playground after a day of sightseeing - or, of course, after a day on the links. Like Austin, San Antonio is home to an impressive roster of outstanding courses.
Some local favourites include the Pecan Valley Golf Club - the venerable host of the 1968 PGA Championship, located in the city's southeast.
North of San Antonio, there's also the Arthur Hills-designed Hill Country Golf Club, offering 27 holes of precision golf at the Hyatt Regency Hill Country Resort. Or hit the Quarry Golf Club in the north-central suburbs, a Keith Foster design where the back nine cuts through a 100-year-old quarry.
A great place to soak up local colour is Canyon Springs Golf Club, with its ranch-style clubhouse built on the spot where stagecoaches made their last stop before heading out of San Antonio. Designed by local architect Thomas Walker, this challenging track, on rolling terrain north of the city, requires patient consideration and the use of every club in the bag.
But the pride of San Antonio golf is found at the Westin La Cantera Resort, a colonial-style, 508-room retreat set high on a bluff north of the downtown. La Cantera's two layouts, the Resort and Palmer courses, rival even the two Fazio jewels at Austin's Barton Creek.
The older and more famous is the Resort Course, a Jay Morrish-Tom Weiskopf collaboration that swoops and dips through the hilly landscape like a runaway roller coaster. Host of the PGA Tour's Valero Texas Open, the course includes at least a dozen unforgettable holes. But the masterwork is the par-four seventh, nicknamed the Rattler, which features a 24-metre drop to a fairway booby-trapped by bunkers and a water hazard.
No less difficult or hilly is the Palmer Course, one of Arnold Palmer's best designs. The King's tight fairways and uneven lies cruelly demand an unending succession of tricky shots.
But all is forgiven on the 18th tee, where weary golfers pause to admire a panoramic view across the heights toward downtown San Antonio and the distant Alamo.
They say there's no prettier sight in all of Texas golf.
Pack your clubs
Air Canada, American Airlines and Continental Airlines offer service from major Canadian cities to Texas. Other major U.S. carriers offer flights to Texas destinations via U.S. gateways. Starting May 1, Air Canada will begin daily service from Toronto to Austin.
Pedernales Golf Club 512-264-1489; http://www.pedernalesgolfclub.com. An eccentric nine-hole layout owned by country music star Willie Nelson. Green fees: $12 to $15 (all figures in U.S. dollars).
Barton Creek Resort 1-800-336-6158; http://www.bartoncreek.com. Play on Barton Creek's four courses is restricted to resort guests.
Fazio Foothills: This brilliant Tom Fazio design sets the standard for Texas resort courses. Green fees: $190 to $250.