But the visitor should not be deceived. The lacklustre contest between the State Treasurer, Kay Bailey Hutchinson, and the Democrat Bob Krueger for the Senate seat made vacant when Lloyd Bentsen was appointed Treasury Secretary may not set local pulses racing. But its implications nationally are huge. Barely a quarter of Texas' registered electorate of 8 million is likely to bother to cast its vote on 5 June. The outcome, though, will be treated as a referendum on Bill Clinton's struggling presidency. The verdict is likely to be scathing.
For an understanding of Mr Clinton's current weakness, there is nowhere better to go than here. He did not carry the state last November. But after his victory, Texans were inclined to look kindly on this apparently moderate Southern Governor from just across the border in Arkansas. Barely six months later, such goodwill has mostly vanished.
Seen through Texas' proud, deeply patriotic prism, this proclaimed 'New Democrat' is turning out to be just another prissy tax-and-spend liberal, whose main priorities are expensive haircuts and allowing homosexuals into the military. 'I wish I'd voted for Bush,' said a woman selling local memorabilia at an emporium called Billy Bond's Texas in Forth Worth's tarted-up Stockyards district. 'Clinton - he's just lip-service and false promises.'
Both the President and Bob Krueger are likely to pay a heavy price next Saturday for such perceived apostasy. Appointed to the Senate last January by the state's popular Democratic Governor Ann Richards, Mr Krueger was originally expected to win comfortably. Instead, in a field of 24 candidates, Ms Hutchinson - neat, composed and personable as an anchor lady on the network news - astonished everyone by pipping him by 500 votes in the first round on 1 May. With Republicans closing ranks around her for the run-off, a poll this week put her almost 20 points ahead.
Assuming she triumphs, history will be made: for the first time since the Civil War, Texas will have two Republican Senators in Washington. For Mr Clinton, the consequences are more immediate. Not only will the propaganda advantages of the Democrats' near-monopoly of women legislators be dented. His precarious hold on the Senate will be further eroded, and Bob Dole, the already cantankerous minority leader, will gain further encouragement to make mischief.
It is easy to sympathise with Bob Krueger's plight. His plodding, erudite style is certainly a handicap: 'You can't quote Shakespeare in Texas and expect to win,' commented one pollster. A far worse one however is the need to distance himself from an unpopular president. In Congress he has been caught in no man's land, torn between party loyalty and the practical impossibility of backing Mr Clinton's deficit cutting package and its planned energy tax, loathed in oil-rich Texas.
In a televised debate in Arlington this week, Ms Hutchinson sweetly skewered him. 'Bob, you didn't vote for the budget, but you didn't have the guts to join with us Republicans and vote against it. You're the only member of the US Senate that voted for nothing.' The applause of the 1,000 audience in the university auditorium here was thunderous. In Texas they don't much go for shilly-shallying.
Now advised by Paul Begala, one of Mr Clinton's most esteemed strategists last autumn, Mr Krueger is trying every expedient to turn the tide. Among the issues, he avoids the economy wherever he can, staking all on health care. But it is no longer he but Ms Hutchinson who can better claim the high ground of Washington outsider; and for the rest there is precious little real daylight between them. Then, notoriously, there are the ads.
Mr Begala is master of the self-deprecating commercial, but his efforts here may be going too far. The viewer squirms in his seat at the vision of Bob Krueger-cum-Arnold Schwarzenegger - a sitting US Senator decked out in leather jacket and Terminator dark glasses: 'Was it Shakespeare who said 'Hasta la vista, Baby ?' ' enquires the English don desperately seeking votes.
Seven days before the election, it is improbable indeed that he will secure enough. Mr Krueger retains the overwhelming support of registered Democrats, and of blacks and Hispanics in the urban centres of Houston, Dallas-Forth Worth, San Antonio and El Paso. But in a state at heart so conservative, this will not be enough. At least not these days, with Bill Clinton in the White House.