When you travel, you've gotta try the local sake.

Literal

Travel [to-に] went [conditional-たら] local-sake [object-を] must-drink.

地酒 (local sake) is sake brewed in the region one is visiting — an important part of Japanese food culture. 飲まなきゃ is a casual contraction of 飲まなければ(ならない) — 'gotta drink.' The たら conditional ('once you've set out') triggers the obligation.