[math-fun] physics thought experiment

You and your buddy have each woken up at some random, unknown point in the milky way galaxy. You have a very bright, omni-directional beacon that can easily be seen from any point inside it's light cone. You can travel in any direction, at any speed up to C (but not exceeding it of course). Your goal is to locate and rendezvous with your buddy for one last drink, sometime before one of you dies of old age. What's your strategy.