Christiansted is a historic Danish-style town that always served as St. Croix's commercial center. Your best bet is to see the historic sights in the morning, when it's still cool. Break for lunch at an open-air restaurant before spending as much time as you like shopping.
In the 1700s and 1800s Christiansted was a trading center for sugar, rum, and molasses. Today there are law offices, tourist shops, and restaurants, but many of the buildings, which start at the harbor and go up the gently sloped hillsides, still date from the 18th century. You can't get lost. All streets lead back downhill to the water.