Exeter is best viewed on foot. Downtown has an eclectic mix of architecture, from clapboarded Georgian homes to intricate brick Victorians. The center of downtown is marked by the Swasey Pavilion, a trim 1916 bandstand with an intricate floral mosaic on the ceiling. Brass-band concerts are still held here in the summer. Just up the hill is the imposing Congregational Church, built in 1798, with its handsome white spire. On Thursdays from mid-June to early October, a farmers' market is held from about 2:15 to 6:30pm, along Swasey Parkway near the river (off Water St.).
The booklet Walking Tour of Exeter, published in 1994 by the Exeter Historical Society, is available for a small fee at the American Independence Museum, the Exeter Chamber of Commerce, and the Exeter Historical Society (located at 47 Front St.); it's well worth a look if you're serious about getting to know the town. This guide (and the map that comes with it) offers a concise, well-written history of the town, with interesting historical and architectural facts about notable buildings (such as 11 Pleasant St., where Abraham Lincoln's son lived while attending Exeter Academy).
With or without the guide, the grounds of Phillips Exeter Academy, just southwest of the town center, are worth a stroll. The predominant style is Georgian-inspired brick -- it's hard to imagine misbehaving at a campus this stern, though that hasn't deterred generations of prep-school kids here -- but look for anomalies, too, such as the 1971 prize-winning library, designed by noted American architect Louis I. Kahn, on Front Street, near Abbot Place.
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