I wouldn't go that far for ordinary coffee. Surely there are places along the way that do regular coffee. Personally I like Caribou (local chain) much better than Starbucks in that the coffee doesn't taste burnt, but it's generally full bodied and might not be what the OP wants. There's a small food court around C12-C10, for instance, as well as various F&B outlets that the OP would pass along the way.

BTW, the A and high C gates are a short flight of stairs down from the rest of the C concourse. Between gates C13 and C12 you need to look for the elevator to the right as you walk from A to C. There should be escalators too in the area, but I often see people walking up/down stairs here and also to go up one more level to the skyway connector to the high G gates. Often these escalators are out of order.