She visited the elderly man at the hospital every day except Sunday.
Literal
She [topic-は] Sunday [except-以外], every-day hospital [to-に] that elderly-person [object-を] visited.
以外 ('other than, except') attaches to a noun to carve out exceptions: 日曜日以外 = 'except Sundays.' 病院に...見舞う uses 見舞う ('visit [a sick or troubled person]') — the verb form parallel to 見舞い (the noun for the visit).