Eastbourne Old Town is the nucleus around which the Victorian resort grew. A quiet cluster of streets around the Church of St Mary the Virgin, it has a completely different character from the seafront: older buildings, a few traditional pubs, independent shops, and the kind of unhurried pace that suggests most of its visitors are locals rather than tourists.
The Church of St Mary dates back to the 12th century and has a good Norman chancel. The Lamb Inn on High Street, which the Atlas Obscura entry notes is older than the Magna Carta, is one of the oldest pubs in Sussex and worth a stop for the atmosphere if not the cuisine. The Old Town sits about a mile inland from the seafront — an easy walk that makes a good circuit combined with the Towner Gallery.