Raleigh has traditionally been lumped with Durham and Chapel Hill as part of the Research Triangle — the land of science, technology and, in the run-up to this month’s N.C.A.A. tournament, college basketball. But this geographic shorthand has become increasingly outdated in recent years, as each city has developed a distinct personality. Today, North Carolina’s capital is awash in entrepreneurial energy from homegrown clothing labels and converted art galleries to craft breweries and ambitious restaurants. More than merely one of the Triangle’s three vertexes, Raleigh is now defining itself as a destination worth exploring on its own merits, regardless of what lies beyond the city limits.