Kennebunkport sits in a particularly useful stretch of the Maine coast, with several worthwhile destinations within an hour by car.
Portland (45 km north) is Maine's largest city and one of the better small cities in the northeastern United States. The Old Port district has excellent restaurants, craft breweries, and independent shops in repurposed 19th-century brick warehouses. The Portland Museum of Art has a strong collection of Winslow Homer and Andrew Wyeth works. Plan a full day.
Ogunquit (20 km south) is another coastal resort town, somewhat smaller than Kennebunkport, with Marginal Way — a mile-long cliff walk above the ocean — and a good beach. The town has a strong arts tradition and the Ogunquit Museum of American Art is worth an hour. Less than 30 minutes by car.
York (30 km south) is quieter and more authentically colonial: the Old York Historical Society preserves several 18th-century buildings, and the beaches at Long Sands and Short Sands are excellent. Cape Neddick Lighthouse (Nubble Light), just off the coast at York Beach, is one of the most photographed lighthouses in New England.
Biddeford (15 km north) has been developing a food and arts scene in its old textile mill buildings over the past decade — a useful stop for a meal on the way to or from Portland. Several good independent restaurants have opened in the mill district.
The White Mountains (New Hampshire, about 90 minutes west) are reachable in half a day, offering hiking, the Mount Washington Cog Railway, and fall colour in September and October.