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The U of A campus is coherently organized, with large grass fields forming a line up through the middle of the campus (as shown above, with the historic Old Main in the middle of campus). In planning my visit, I simply made mental notes of whether a particular building was to the right or left of the grass strip.
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The Student Union, a modern, multi-building complex with a spectacular bookstore, is just off the grass strip, near Old Main.
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Across the grass from the Student Union is another impressive modern structure, the new Chemistry building.
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The area adjacent to the main campus entrance, known as Main Gate Square, has a lot of typical college-town amenities, such as restaurants and stores selling school clothing. The above photo looks down University Ave., as one moves away from the campus entrance at University and Park Ave.
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There's another nice bookstore just off campus (shown in foreground to the right, with the campus off to the left), selling all the U of A Wildcat paraphernalia you could want, as well as textbooks. The off-campus store is located in yet another modern facility, the Marshall Building.
Unless you love scorching temperatures, I would suggest you visit the U of A in winter (and even then it was fairly warm, reaching 80 degrees during my visit).