The best time to visit Newark is during the university's academic year, roughly September to May, when the town is fully alive with students and the restaurants, bars, and campus are all buzzing. Fall — September through October — is particularly good: pleasant weather, the campus looking its best, and the trails at White Clay Creek State Park in fine shape for hiking.
Summer is quieter. Many students leave, Main Street loses much of its energy, and some businesses scale back. It is still perfectly fine to visit, just do not expect the same atmosphere.
Graduation in May brings crowds and a festive atmosphere to the campus, but accommodation nearby fills up fast.