Acre is the obvious one — the walled Crusader and Ottoman port across the bay, half an hour by train or car. Allow most of a day for the old city, the subterranean Hospitaller halls, and the rooftop walks.
Caesarea, an hour south down the coast, has the most extensive Roman ruins in Israel — a hippodrome, theatre, and harbour fortifications, all on a stretch of beach. Combine with the colourful artists' colony at Ein Hod on the way back.
Further afield: the Bahá'í gardens have a sister site at Bahji, just outside Acre, with the founder's shrine. Rosh Hanikra, on the Lebanese border, has dramatic limestone sea grottoes reached by cable car. Nazareth and the Sea of Galilee are an hour east and make a long day each.