Raleigh

Raleigh needs 1 day: touring the North Carolina Museum of Natural Sciences, the largest museum in the Southeast and free to enter, and strolling through the historic North Carolina State University campus, the same afternoon. April-June and September-October bring the mildest weather. It's inexpensive for a state capital. It's one of the three cities forming the Research Triangle along with Durham and Chapel Hill -named for the area's high concentration of universities and tech research-, comparable in concept to Silicon Valley but focused on biotech.