Pevensey Castle is one of the strongest historical day trips from Eastbourne. Its outer walls began as a Roman Saxon Shore fort, and after William the Conqueror landed nearby in 1066 the Normans reused the enclosure for a castle, layering one invasion story on top of another.
The ruins are open and readable, with enough surviving stonework to make the defensive plan clear. Combine it with Pevensey village or the coast if you want a slower outing; the castle itself rewards anyone interested in the long military history of southeast England.