"See America." When I got a job in Massachusetts I thought I would be able to take the ad's advice. But it was a year before I got very far out of Boston. At last, when I began a 30-day, 20-lecture tour of scattered campuses around the country, I thought, "Now's my chance". But pretty much all I saw were airports and lecture rooms. The nicest airport was in Cincinnati. The best-equipped lecture rooms were at Ohio State.

I did manage one tourist excursion. In Memphis, my hosts took me to Graceland: suitable revenge for readers who resented the space I gave Elvis Presley - more than to Mozart or Wagner - in one of my books. I was disappointed. Though majestically kitsch, Elvis's home is a suburban villa of modest proportions, whereas I had hoped for something extravagantly vast. In Little Rock, Arkansas, I had no time for tourism, but I stayed in the hotel where Bill Clinton allegedly propositioned Paula Jones. So I saw two great monuments of US history.

Yet, despite the gaps in my sightseeing, I did take in visits to sites of far greater significance for understanding the country's past and future: heroic, unusual, often underprivileged universities that do a magnificent job. Eastern Nazarene College, near Boston, is dedicated to educating members of a small communion of Methodist descent. The history department has only three full-time professors, but they are accommodated in premises that are lovingly looked after. They teach ambitiously wide-ranging courses. The classes I attended were vibrant and entertaining. At Salem State College, the teachers exude fun and are overflowing with innovative ideas and techniques for the classroom. Northern Kentucky University operates on a tight budget and pitches its appeal mainly to local students of modest means, but the professoriate is enthusiastic and endlessly committed. The undergraduate history society has won a national competition for the best history society for 14 of the past 15 years. At Jackson State University in Mississippi, I found intriguing and original interdisciplinary discussions in progress among academics with a real vocation for teaching, and an inexhaustible appetite among the students for asking interesting questions. The University at Buffalo has some of the dreariest buildings and some of the liveliest and most stimulating classes I have seen. At Colorado State University, Fort Collins, I met the most helpful, best humoured and best mannered students I have ever lectured to.

The University of Arkansas, Little Rock, and the University of Memphis are, in essence, urban colleges providing a local service. But it was a pleasure to be on their well-designed campuses, with eager students and interesting graduate programmes. At all these places, I met scholars whose work I knew and admired.

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More extraordinary, and at least as impressive, were the US Air Force and Naval academies, respectively in Colorado Springs and Annapolis, Maryland.

Neither endures severe budgetary constraint, but they operate under their own difficulties. Annapolis suffers from being close to Washington DC and is inevitably attractive to a commander-in-chief in search of a captive audience in smart uniforms. And there are obvious problems in cultivating academic open-mindedness and military discipline simultaneously. At Colorado Springs, freshmen have to march between classes and are not allowed off the premises. Both institutions do a brilliant job of producing intellectually vigorous, critically questioning young people for their country's armed services. The classroom seems to benefit from being an environment in which students can challenge superior officers in ways not permitted on the parade ground. The cultural and academic formation available is - unlike those offered at corresponding institutions in Europe - on a par with the world's best universities. The settings of both academies are inspiringly beautiful. At Colorado Springs, the uncompromisingly angular, rationalist architecture intersects with the weathered antiquity of the Rocky Mountains. At Annapolis, the dignified, domed buildings of grey stone blend with the charm of the colonial city that surrounds them and with the ocean beyond.

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The Ivies and their ilk ensure that the US has the world's best universities. But it is the excellence of those that are more modestly ranked, or dedicated to peculiar constituencies, that constitutes the true greatness of America's higher education. They are, perhaps, the hope of the world. The world desperately needs a well-educated superpower. So far, US universities have not delivered this vital requisite: if they had, we would not have had to put up with George W. Bush's iniquities and inanities. But the places I saw on my tour are taking the obligation seriously and are working on it sedulously.

Felipe Fern¨¤ndez-Armesto is Prince of Asturias professor of history at Tufts University in the US.