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I'm just heading out for a quick coffee nearby.
Literal
Just there-until coffee [obj-を] drink [to-に] go.
ちょっとそこまで is a stock dismissive phrase for 'just a quick step out / just somewhere nearby,' often used when explaining a brief errand or outing without specifying where. 飲みに行く 'go to drink' uses the masu-stem + に行く purpose-of-motion pattern, marking the verb-stem as the goal of motion.