After dinner, Father went out jogging.

Literal

Dinner-after, father [topic-は] jogging [to-に] go-out-[past-た].

ジョギングに出かける is a common construction: the destination-ish に marks the purpose ('for jogging'), and 出かける ('to go out, set out') is more specific than plain 行く. A tidy illustration of the purpose-に pattern with activity nouns.